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// * the Geant4 Collaboration.  It is provided  under  the terms  and *
// * conditions of the Geant4 Software License,  included in the file *
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//
// neutron_hp -- source file
// J.P. Wellisch, Nov-1996
// A prototype of the low energy neutron transport model.
// P. Arce, June-2014 Conversion neutron_hp to particle_hp
//
#include "G4ParticleHPFastLegendre.hh"

const G4double
  G4ParticleHPFastLegendre::l18[3801] = {1, 0.911993, 0.827896,
  0.747593, 0.670972, 0.597923, 0.528338, 0.462112, 0.399144,
  0.339331, 0.282575, 0.228782, 0.177856, 0.129705, 0.0842414,
  0.041376, 0.00102344, -0.0368998, -0.0724754, -0.105783, -0.136901,
  -0.165905, -0.192869, -0.217866, -0.240966, -0.262239, -0.281751,
  -0.299569, -0.315756, -0.330375, -0.343486, -0.35515, -0.365423,
  -0.374362, -0.382022, -0.388456, -0.393717, -0.397855, -0.400919,
  -0.402958, -0.404018, -0.404145, -0.403383, -0.401774, -0.399362,
  -0.396186, -0.392285, -0.387699, -0.382464, -0.376617, -0.370193,
  -0.363226, -0.355749, -0.347794, -0.339392, -0.330573, -0.321367,
  -0.311802, -0.301906, -0.291704, -0.281222, -0.270486, -0.25952,
  -0.248346, -0.236987, -0.225464, -0.2138, -0.202013, -0.190123,
  -0.17815, -0.166111, -0.154023, -0.141903, -0.129768, -0.117632,
  -0.105512, -0.09342, -0.0813709, -0.0693777, -0.0574528, -0.0456083,
  -0.0338557, -0.0222059, -0.0106695, 0.000743643, 0.0120239,
  0.0231624, 0.0341504, 0.0449798, 0.0556429, 0.0661325, 0.0764415,
  0.0865637, 0.0964928, 0.106223, 0.115749, 0.125067, 0.13417,
  0.143056, 0.151719, 0.160157, 0.168366, 0.176342, 0.184084,
  0.191589, 0.198854, 0.205878, 0.212659, 0.219195, 0.225486, 0.23153,
  0.237327, 0.242876, 0.248177, 0.25323, 0.258035, 0.262592, 0.266902,
  0.270966, 0.274784, 0.278357, 0.281687, 0.284775, 0.287623,
  0.290231, 0.292603, 0.294739, 0.296642, 0.298314, 0.299757,
  0.300974, 0.301967, 0.302738, 0.303291, 0.303628, 0.303751,
  0.303665, 0.303372, 0.302874, 0.302176, 0.301281, 0.300191, 0.29891,
  0.297442, 0.295789, 0.293957, 0.291947, 0.289764, 0.287411,
  0.284892, 0.282211, 0.279371, 0.276376, 0.27323, 0.269937, 0.2665,
  0.262924, 0.259211, 0.255367, 0.251395, 0.247299, 0.243082,
  0.238748, 0.234302, 0.229747, 0.225088, 0.220327, 0.215469,
  0.210517, 0.205476, 0.200349, 0.19514, 0.189852, 0.184491, 0.179058,
  0.173558, 0.167994, 0.162371, 0.156692, 0.15096, 0.145178, 0.139352,
  0.133483, 0.127575, 0.121633, 0.115658, 0.109656, 0.103628,
  0.097578, 0.0915096, 0.0854259, 0.0793299, 0.0732248, 0.0671137,
  0.0609996, 0.0548855, 0.0487743, 0.042669, 0.0365724, 0.0304874,
  0.0244166, 0.0183629, 0.0123288, 0.00631714, 0.000330371,
  -0.00562893, -0.0115583, -0.0174552, -0.0233174, -0.0291424,
  -0.034928, -0.0406719, -0.0463719, -0.0520259, -0.0576317,
  -0.0631873, -0.0686907, -0.07414, -0.0795331, -0.0848683,
  -0.0901438, -0.0953577, -0.100508, -0.105594, -0.110614, -0.115565,
  -0.120446, -0.125257, -0.129995, -0.134659, -0.139248, -0.14376,
  -0.148195, -0.152551, -0.156826, -0.161021, -0.165133, -0.169162,
  -0.173107, -0.176967, -0.18074, -0.184427, -0.188026, -0.191537,
  -0.194959, -0.198291, -0.201532, -0.204683, -0.207742, -0.210709,
  -0.213584, -0.216366, -0.219055, -0.221651, -0.224152, -0.22656,
  -0.228873, -0.231091, -0.233215, -0.235245, -0.237179, -0.239019,
  -0.240764, -0.242414, -0.243969, -0.245429, -0.246795, -0.248067,
  -0.249244, -0.250328, -0.251318, -0.252214, -0.253017, -0.253728,
  -0.254346, -0.254872, -0.255307, -0.255651, -0.255904, -0.256067,
  -0.25614, -0.256125, -0.256021, -0.255829, -0.25555, -0.255185,
  -0.254734, -0.254198, -0.253577, -0.252873, -0.252086, -0.251217,
  -0.250266, -0.249236, -0.248125, -0.246936, -0.245669, -0.244325,
  -0.242905, -0.24141, -0.23984, -0.238198, -0.236483, -0.234697,
  -0.23284, -0.230915, -0.228921, -0.22686, -0.224733, -0.22254,
  -0.220284, -0.217965, -0.215584, -0.213143, -0.210641, -0.208082,
  -0.205464, -0.202791, -0.200063, -0.197281, -0.194446, -0.191559,
  -0.188622, -0.185636, -0.182601, -0.17952, -0.176393, -0.173221,
  -0.170007, -0.16675, -0.163452, -0.160114, -0.156738, -0.153325,
  -0.149875, -0.146391, -0.142873, -0.139322, -0.13574, -0.132128,
  -0.128488, -0.124819, -0.121124, -0.117404, -0.11366, -0.109893,
  -0.106104, -0.102295, -0.0984663, -0.0946196, -0.090756, -0.0868767,
  -0.0829827, -0.0790753, -0.0751556, -0.0712249, -0.0672841,
  -0.0633345, -0.0593772, -0.0554134, -0.0514441, -0.0474704,
  -0.0434936, -0.0395146, -0.0355346, -0.0315547, -0.0275759,
  -0.0235993, -0.0196259, -0.0156569, -0.0116933, -0.00773601,
  -0.00378618, 0.000155205, 0.00408715, 0.00800865, 0.0119187,
  0.0158164, 0.0197007, 0.0235706, 0.0274253, 0.0312637, 0.0350851,
  0.0388883, 0.0426726, 0.0464371, 0.0501808, 0.053903, 0.0576026,
  0.061279, 0.0649312, 0.0685585, 0.07216, 0.0757349, 0.0792825,
  0.0828019, 0.0862924, 0.0897533, 0.0931838, 0.0965831, 0.0999507,
  0.103286, 0.106588, 0.109855, 0.113089, 0.116287, 0.119449,
  0.122575, 0.125664, 0.128715, 0.131728, 0.134702, 0.137637,
  0.140531, 0.143386, 0.146199, 0.148971, 0.1517, 0.154388, 0.157032,
  0.159633, 0.16219, 0.164703, 0.167171, 0.169594, 0.171972, 0.174304,
  0.176589, 0.178828, 0.18102, 0.183165, 0.185263, 0.187312, 0.189314,
  0.191267, 0.193171, 0.195027, 0.196833, 0.19859, 0.200297, 0.201955,
  0.203563, 0.20512, 0.206628, 0.208085, 0.209491, 0.210847, 0.212152,
  0.213406, 0.214609, 0.215761, 0.216862, 0.217911, 0.21891, 0.219857,
  0.220753, 0.221598, 0.222392, 0.223134, 0.223825, 0.224465,
  0.225054, 0.225591, 0.226078, 0.226514, 0.226899, 0.227233,
  0.227517, 0.227751, 0.227933, 0.228066, 0.228149, 0.228182,
  0.228165, 0.228099, 0.227983, 0.227818, 0.227605, 0.227342,
  0.227032, 0.226673, 0.226266, 0.225811, 0.225309, 0.22476, 0.224163,
  0.223521, 0.222832, 0.222097, 0.221316, 0.22049, 0.219619, 0.218703,
  0.217743, 0.216739, 0.215691, 0.2146, 0.213466, 0.21229, 0.211072,
  0.209812, 0.20851, 0.207168, 0.205785, 0.204362, 0.202899, 0.201398,
  0.199857, 0.198278, 0.196661, 0.195007, 0.193316, 0.191588,
  0.189825, 0.188025, 0.186191, 0.184322, 0.182419, 0.180482,
  0.178512, 0.176509, 0.174475, 0.172409, 0.170311, 0.168183,
  0.166025, 0.163838, 0.161621, 0.159376, 0.157103, 0.154802,
  0.152475, 0.150121, 0.147742, 0.145337, 0.142907, 0.140454,
  0.137976, 0.135476, 0.132953, 0.130408, 0.127842, 0.125255,
  0.122648, 0.120021, 0.117375, 0.11471, 0.112028, 0.109328, 0.106611,
  0.103877, 0.101128, 0.098364, 0.0955852, 0.0927924, 0.0899861,
  0.087167, 0.0843355, 0.0814923, 0.0786379, 0.0757729, 0.0728978,
  0.0700133, 0.0671199, 0.0642181, 0.0613085, 0.0583917, 0.0554683,
  0.0525388, 0.0496037, 0.0466637, 0.0437192, 0.0407709, 0.0378193,
  0.0348649, 0.0319083, 0.0289501, 0.0259907, 0.0230308, 0.0200709,
  0.0171114, 0.014153, 0.0111962, 0.00824154, 0.00528949, 0.00234062,
  -0.000604559, -0.00354552, -0.00648175, -0.00941273, -0.0123379,
  -0.0152569, -0.0181691, -0.021074, -0.0239711, -0.0268599, -0.02974,
  -0.0326108, -0.0354719, -0.0383228, -0.0411629, -0.0439919,
  -0.0468093, -0.0496146, -0.0524072, -0.0551869, -0.0579531,
  -0.0607053, -0.0634432, -0.0661663, -0.0688741, -0.0715662,
  -0.0742422, -0.0769017, -0.0795442, -0.0821694, -0.0847768,
  -0.087366, -0.0899366, -0.0924882, -0.0950204, -0.0975329,
  -0.100025, -0.102497, -0.104948, -0.107378, -0.109786, -0.112172,
  -0.114536, -0.116877, -0.119195, -0.12149, -0.123761, -0.126008,
  -0.128231, -0.130429, -0.132602, -0.13475, -0.136872, -0.138969,
  -0.141039, -0.143083, -0.145101, -0.147091, -0.149054, -0.15099,
  -0.152898, -0.154778, -0.156629, -0.158453, -0.160247, -0.162013,
  -0.163749, -0.165456, -0.167133, -0.168781, -0.170398, -0.171986,
  -0.173543, -0.175069, -0.176565, -0.17803, -0.179464, -0.180866,
  -0.182237, -0.183577, -0.184885, -0.186161, -0.187405, -0.188617,
  -0.189797, -0.190945, -0.19206, -0.193142, -0.194192, -0.195209,
  -0.196194, -0.197145, -0.198064, -0.198949, -0.199802, -0.200621,
  -0.201407, -0.20216, -0.202879, -0.203565, -0.204218, -0.204837,
  -0.205423, -0.205975, -0.206494, -0.20698, -0.207432, -0.20785,
  -0.208235, -0.208587, -0.208905, -0.209189, -0.209441, -0.209659,
  -0.209843, -0.209995, -0.210113, -0.210198, -0.21025, -0.210269,
  -0.210255, -0.210208, -0.210129, -0.210016, -0.209871, -0.209693,
  -0.209483, -0.209241, -0.208966, -0.20866, -0.208321, -0.20795,
  -0.207548, -0.207114, -0.206648, -0.206152, -0.205623, -0.205064,
  -0.204474, -0.203853, -0.203202, -0.20252, -0.201808, -0.201066,
  -0.200294, -0.199492, -0.19866, -0.197799, -0.196909, -0.19599,
  -0.195043, -0.194066, -0.193061, -0.192029, -0.190968, -0.189879,
  -0.188763, -0.187619, -0.186449, -0.185252, -0.184028, -0.182777,
  -0.181501, -0.180198, -0.17887, -0.177517, -0.176139, -0.174735,
  -0.173307, -0.171855, -0.170378, -0.168878, -0.167354, -0.165807,
  -0.164236, -0.162643, -0.161028, -0.15939, -0.15773, -0.156049,
  -0.154347, -0.152623, -0.150879, -0.149114, -0.147329, -0.145524,
  -0.1437, -0.141856, -0.139994, -0.138113, -0.136213, -0.134296,
  -0.13236, -0.130408, -0.128438, -0.126451, -0.124448, -0.122429,
  -0.120394, -0.118344, -0.116278, -0.114198, -0.112103, -0.109994,
  -0.107871, -0.105735, -0.103585, -0.101423, -0.0992475, -0.0970603,
  -0.0948612, -0.0926505, -0.0904287, -0.088196, -0.0859527,
  -0.0836993, -0.0814361, -0.0791633, -0.0768813, -0.0745906,
  -0.0722913, -0.0699838, -0.0676686, -0.0653459, -0.063016,
  -0.0606793, -0.0583362, -0.055987, -0.0536319, -0.0512715,
  -0.0489059, -0.0465356, -0.0441608, -0.041782, -0.0393994,
  -0.0370134, -0.0346244, -0.0322326, -0.0298384, -0.0274422,
  -0.0250442, -0.0226449, -0.0202445, -0.0178434, -0.0154418,
  -0.0130403, -0.010639, -0.00823827, -0.00583851, -0.00344001,
  -0.00104309, 0.00135191, 0.00374468, 0.00613488, 0.0085222,
  0.0109063, 0.0132869, 0.0156636, 0.0180362, 0.0204043, 0.0227676,
  0.0251258, 0.0274786, 0.0298256, 0.0321666, 0.0345013, 0.0368293,
  0.0391504, 0.0414642, 0.0437704, 0.0460688, 0.0483591, 0.0506409,
  0.0529139, 0.0551779, 0.0574326, 0.0596777, 0.0619129, 0.0641379,
  0.0663524, 0.0685563, 0.070749, 0.0729306, 0.0751005, 0.0772586,
  0.0794046, 0.0815382, 0.0836592, 0.0857673, 0.0878622, 0.0899438,
  0.0920116, 0.0940656, 0.0961053, 0.0981307, 0.100141, 0.102137,
  0.104118, 0.106083, 0.108033, 0.109966, 0.111884, 0.113786, 0.11567,
  0.117539, 0.11939, 0.121224, 0.12304, 0.124839, 0.12662, 0.128383,
  0.130128, 0.131855, 0.133563, 0.135252, 0.136922, 0.138572,
  0.140204, 0.141816, 0.143408, 0.14498, 0.146532, 0.148064, 0.149575,
  0.151066, 0.152536, 0.153985, 0.155413, 0.15682, 0.158205, 0.159569,
  0.160912, 0.162232, 0.163531, 0.164807, 0.166061, 0.167293,
  0.168502, 0.169689, 0.170853, 0.171995, 0.173113, 0.174208,
  0.175281, 0.17633, 0.177355, 0.178357, 0.179336, 0.180291, 0.181222,
  0.18213, 0.183013, 0.183873, 0.184709, 0.18552, 0.186308, 0.187071,
  0.187809, 0.188524, 0.189214, 0.18988, 0.190521, 0.191137, 0.191729,
  0.192296, 0.192839, 0.193357, 0.19385, 0.194318, 0.194762, 0.19518,
  0.195574, 0.195943, 0.196288, 0.196607, 0.196901, 0.197171,
  0.197416, 0.197636, 0.19783, 0.198001, 0.198146, 0.198266, 0.198362,
  0.198433, 0.198479, 0.1985, 0.198497, 0.198469, 0.198416, 0.198339,
  0.198237, 0.198111, 0.19796, 0.197785, 0.197585, 0.197362, 0.197114,
  0.196841, 0.196545, 0.196225, 0.19588, 0.195512, 0.19512, 0.194704,
  0.194265, 0.193802, 0.193315, 0.192806, 0.192272, 0.191716,
  0.191137, 0.190534, 0.189909, 0.18926, 0.188589, 0.187896, 0.18718,
  0.186442, 0.185681, 0.184898, 0.184094, 0.183267, 0.182419,
  0.181549, 0.180658, 0.179745, 0.178811, 0.177856, 0.17688, 0.175884,
  0.174866, 0.173829, 0.17277, 0.171692, 0.170594, 0.169476, 0.168338,
  0.16718, 0.166003, 0.164807, 0.163592, 0.162358, 0.161105, 0.159834,
  0.158544, 0.157236, 0.15591, 0.154566, 0.153205, 0.151826, 0.150429,
  0.149016, 0.147586, 0.146139, 0.144675, 0.143195, 0.141699,
  0.140187, 0.138659, 0.137116, 0.135557, 0.133984, 0.132395,
  0.130791, 0.129173, 0.127541, 0.125894, 0.124234, 0.12256, 0.120872,
  0.119171, 0.117457, 0.11573, 0.113991, 0.112239, 0.110475, 0.108699,
  0.106911, 0.105111, 0.103301, 0.101479, 0.0996464, 0.0978032,
  0.0959496, 0.0940858, 0.092212, 0.0903285, 0.0884356, 0.0865333,
  0.0846221, 0.082702, 0.0807734, 0.0788365, 0.0768914, 0.0749385,
  0.072978, 0.07101, 0.0690349, 0.0670529, 0.0650642, 0.0630691,
  0.0610677, 0.0590604, 0.0570473, 0.0550287, 0.0530049, 0.050976,
  0.0489424, 0.0469042, 0.0448617, 0.0428152, 0.0407648, 0.0387108,
  0.0366535, 0.034593, 0.0325297, 0.0304638, 0.0283954, 0.0263249,
  0.0242525, 0.0221784, 0.0201029, 0.0180261, 0.0159484, 0.01387,
  0.0117911, 0.00971193, 0.00763274, 0.00555377, 0.00347526,
  0.00139744, -0.000679458, -0.00275519, -0.00482953, -0.00690224,
  -0.0089731, -0.0110419, -0.0131083, -0.0151722, -0.0172333,
  -0.0192913, -0.0213462, -0.0233975, -0.0254452, -0.0274889,
  -0.0295285, -0.0315637, -0.0335942, -0.03562, -0.0376407,
  -0.0396561, -0.0416661, -0.0436703, -0.0456686, -0.0476607,
  -0.0496465, -0.0516257, -0.0535981, -0.0555635, -0.0575217,
  -0.0594724, -0.0614154, -0.0633507, -0.0652778, -0.0671967,
  -0.0691071, -0.0710088, -0.0729016, -0.0747854, -0.0766598,
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  -0.0233174, -0.0174552, -0.0115583, -0.00562893, 0.000330371,
  0.00631714, 0.0123288, 0.0183629, 0.0244166, 0.0304874, 0.0365724,
  0.042669, 0.0487743, 0.0548855, 0.0609996, 0.0671137, 0.0732248,
  0.0793299, 0.0854259, 0.0915096, 0.097578, 0.103628, 0.109656,
  0.115658, 0.121633, 0.127575, 0.133483, 0.139352, 0.145178, 0.15096,
  0.156692, 0.162371, 0.167994, 0.173558, 0.179058, 0.184491,
  0.189852, 0.19514, 0.200349, 0.205476, 0.210517, 0.215469, 0.220327,
  0.225088, 0.229747, 0.234302, 0.238748, 0.243082, 0.247299,
  0.251395, 0.255367, 0.259211, 0.262924, 0.2665, 0.269937, 0.27323,
  0.276376, 0.279371, 0.282211, 0.284892, 0.287411, 0.289764,
  0.291947, 0.293957, 0.295789, 0.297442, 0.29891, 0.300191, 0.301281,
  0.302176, 0.302874, 0.303372, 0.303665, 0.303751, 0.303628,
  0.303291, 0.302738, 0.301967, 0.300974, 0.299757, 0.298314,
  0.296642, 0.294739, 0.292603, 0.290231, 0.287623, 0.284775,
  0.281687, 0.278357, 0.274784, 0.270966, 0.266902, 0.262592,
  0.258035, 0.25323, 0.248177, 0.242876, 0.237327, 0.23153, 0.225486,
  0.219195, 0.212659, 0.205878, 0.198854, 0.191589, 0.184084,
  0.176342, 0.168366, 0.160157, 0.151719, 0.143056, 0.13417, 0.125067,
  0.115749, 0.106223, 0.0964928, 0.0865637, 0.0764415, 0.0661325,
  0.0556429, 0.0449798, 0.0341504, 0.0231624, 0.0120239, 0.000743643,
  -0.0106695, -0.0222059, -0.0338557, -0.0456083, -0.0574528,
  -0.0693777, -0.0813709, -0.09342, -0.105512, -0.117632, -0.129768,
  -0.141903, -0.154023, -0.166111, -0.17815, -0.190123, -0.202013,
  -0.2138, -0.225464, -0.236987, -0.248346, -0.25952, -0.270486,
  -0.281222, -0.291704, -0.301906, -0.311802, -0.321367, -0.330573,
  -0.339392, -0.347794, -0.355749, -0.363226, -0.370193, -0.376617,
  -0.382464, -0.387699, -0.392285, -0.396186, -0.399362, -0.401774,
  -0.403383, -0.404145, -0.404018, -0.402958, -0.400919, -0.397855,
  -0.393717, -0.388456, -0.382022, -0.374362, -0.365423, -0.35515,
  -0.343486, -0.330375, -0.315756, -0.299569, -0.281751, -0.262239,
  -0.240966, -0.217866, -0.192869, -0.165905, -0.136901, -0.105783,
  -0.0724754, -0.0368998, 0.00102344, 0.041376, 0.0842414, 0.129705,
  0.177856, 0.228782, 0.282575, 0.339331, 0.399144, 0.462112,
  0.528338, 0.597923, 0.670972, 0.747593, 0.827896, 0.911993, 1};
  const G4double G4ParticleHPFastLegendre::i18[3801] = {0, 0.000502977,
  0.000960668, 0.0013751, 0.00174824, 0.002082, 0.00237823,
  0.00263873, 0.00286523, 0.00305943, 0.00322295, 0.00335739,
  0.00346427, 0.00354508, 0.00360126, 0.0036342, 0.00364525,
  0.0036357, 0.00360681, 0.0035598, 0.00349584, 0.00341606,
  0.00332156, 0.00321338, 0.00309255, 0.00296005, 0.00281682,
  0.00266376, 0.00250176, 0.00233166, 0.00215426, 0.00197034,
  0.00178066, 0.00158592, 0.00138681, 0.001184, 0.000978115,
  0.000769757, 0.000559506, 0.000347914, 0.000135508, -7.72072e-05,
  -0.000289754, -0.000501675, -0.000712535, -0.000921923, -0.00112945,
  -0.00133474, -0.00153744, -0.00173723, -0.00193378, -0.00212681,
  -0.00231603, -0.0025012, -0.00268206, -0.00285838, -0.00302996,
  -0.0031966, -0.00335812, -0.00351434, -0.00366513, -0.00381032,
  -0.00394981, -0.00408347, -0.00421119, -0.0043329, -0.0044485,
  -0.00455793, -0.00466113, -0.00475804, -0.00484864, -0.00493289,
  -0.00501076, -0.00508226, -0.00514736, -0.00520608, -0.00525843,
  -0.00530443, -0.0053441, -0.00537747, -0.00540459, -0.00542549,
  -0.00544024, -0.00544889, -0.00545149, -0.00544813, -0.00543886,
  -0.00542377, -0.00540294, -0.00537645, -0.0053444, -0.00530687,
  -0.00526397, -0.00521579, -0.00516243, -0.00510401, -0.00504062,
  -0.00497239, -0.00489943, -0.00482185, -0.00473977, -0.0046533,
  -0.00456258, -0.00446772, -0.00436885, -0.00426609, -0.00415957,
  -0.00404942, -0.00393576, -0.00381873, -0.00369845, -0.00357505,
  -0.00344867, -0.00331944, -0.00318748, -0.00305292, -0.0029159,
  -0.00277655, -0.002635, -0.00249137, -0.00234579, -0.0021984,
  -0.00204932, -0.00189868, -0.0017466, -0.00159321, -0.00143864,
  -0.001283, -0.00112643, -0.000969028, -0.000810931, -0.000652252,
  -0.00049311, -0.000333619, -0.000173894, -1.40474e-05, 0.000145808,
  0.000305564, 0.000465112, 0.000624345, 0.000783158, 0.000941449,
  0.00109912, 0.00125606, 0.00141218, 0.00156738, 0.00172158,
  0.00187467, 0.00202656, 0.00217718, 0.00232642, 0.00247421,
  0.00262047, 0.00276511, 0.00290805, 0.00304923, 0.00318856,
  0.00332597, 0.00346139, 0.00359475, 0.00372599, 0.00385504,
  0.00398185, 0.00410634, 0.00422846, 0.00434816, 0.00446538,
  0.00458007, 0.00469217, 0.00480165, 0.00490845, 0.00501253,
  0.00511384, 0.00521236, 0.00530803, 0.00540083, 0.00549071,
  0.00557766, 0.00566162, 0.00574259, 0.00582052, 0.0058954,
  0.0059672, 0.0060359, 0.00610148, 0.00616393, 0.00622322,
  0.00627935, 0.0063323, 0.00638206, 0.00642862, 0.00647198,
  0.00651213, 0.00654906, 0.00658277, 0.00661327, 0.00664055,
  0.00666461, 0.00668546, 0.00670311, 0.00671756, 0.00672881,
  0.00673689, 0.0067418, 0.00674354, 0.00674215, 0.00673762,
  0.00672999, 0.00671926, 0.00670545, 0.00668859, 0.00666869,
  0.00664578, 0.00661989, 0.00659103, 0.00655923, 0.00652452,
  0.00648693, 0.00644649, 0.00640322, 0.00635717, 0.00630835,
  0.0062568, 0.00620256, 0.00614566, 0.00608614, 0.00602402,
  0.00595936, 0.00589219, 0.00582254, 0.00575045, 0.00567597,
  0.00559914, 0.00551999, 0.00543857, 0.00535493, 0.00526909,
  0.00518112, 0.00509104, 0.00499891, 0.00490478, 0.00480868,
  0.00471066, 0.00461077, 0.00450906, 0.00440556, 0.00430034,
  0.00419344, 0.0040849, 0.00397478, 0.00386312, 0.00374997,
  0.00363538, 0.0035194, 0.00340208, 0.00328347, 0.00316361,
  0.00304257, 0.00292038, 0.00279709, 0.00267277, 0.00254745,
  0.00242118, 0.00229403, 0.00216603, 0.00203724, 0.0019077,
  0.00177747, 0.00164659, 0.00151512, 0.00138311, 0.00125059,
  0.00111763, 0.000984275, 0.000850567, 0.000716558, 0.000582296,
  0.00044783, 0.000313206, 0.000178473, 4.36775e-05, -9.11331e-05,
  -0.000225912, -0.000360613, -0.000495191, -0.000629599,
  -0.000763792, -0.000897725, -0.00103135, -0.00116463, -0.00129752,
  -0.00142997, -0.00156195, -0.0016934, -0.00182429, -0.00195457,
  -0.0020842, -0.00221315, -0.00234138, -0.00246883, -0.00259548,
  -0.00272128, -0.0028462, -0.0029702, -0.00309324, -0.00321528,
  -0.00333629, -0.00345624, -0.00357508, -0.00369279, -0.00380932,
  -0.00392466, -0.00403875, -0.00415158, -0.0042631, -0.00437329,
  -0.00448212, -0.00458956, -0.00469558, -0.00480015, -0.00490323,
  -0.00500482, -0.00510487, -0.00520336, -0.00530026, -0.00539556,
  -0.00548922, -0.00558123, -0.00567155, -0.00576018, -0.00584707,
  -0.00593222, -0.00601561, -0.0060972, -0.006177, -0.00625496,
  -0.00633109, -0.00640535, -0.00647774, -0.00654823, -0.00661681,
  -0.00668347, -0.0067482, -0.00681097, -0.00687178, -0.00693061,
  -0.00698745, -0.00704229, -0.00709512, -0.00714594, -0.00719472,
  -0.00724147, -0.00728617, -0.00732882, -0.0073694, -0.00740792,
  -0.00744437, -0.00747875, -0.00751104, -0.00754125, -0.00756937,
  -0.0075954, -0.00761934, -0.00764118, -0.00766093, -0.00767859,
  -0.00769415, -0.00770762, -0.00771899, -0.00772827, -0.00773547,
  -0.00774058, -0.00774362, -0.00774457, -0.00774345, -0.00774027,
  -0.00773503, -0.00772773, -0.00771838, -0.00770699, -0.00769357,
  -0.00767813, -0.00766067, -0.0076412, -0.00761973, -0.00759628,
  -0.00757086, -0.00754346, -0.00751412, -0.00748283, -0.00744962,
  -0.00741449, -0.00737746, -0.00733854, -0.00729774, -0.00725509,
  -0.00721059, -0.00716426, -0.00711611, -0.00706617, -0.00701445,
  -0.00696097, -0.00690574, -0.00684878, -0.00679011, -0.00672974,
  -0.0066677, -0.00660401, -0.00653868, -0.00647174, -0.0064032,
  -0.00633309, -0.00626142, -0.00618821, -0.0061135, -0.00603729,
  -0.00595961, -0.00588048, -0.00579993, -0.00571798, -0.00563464,
  -0.00554995, -0.00546392, -0.00537659, -0.00528796, -0.00519808,
  -0.00510695, -0.00501461, -0.00492107, -0.00482637, -0.00473053,
  -0.00463358, -0.00453553, -0.00443641, -0.00433626, -0.00423509,
  -0.00413293, -0.00402981, -0.00392575, -0.00382077, -0.00371492,
  -0.0036082, -0.00350065, -0.00339229, -0.00328315, -0.00317326,
  -0.00306264, -0.00295133, -0.00283934, -0.0027267, -0.00261344,
  -0.00249959, -0.00238517, -0.00227022, -0.00215475, -0.0020388,
  -0.00192239, -0.00180555, -0.0016883, -0.00157068, -0.0014527,
  -0.00133441, -0.00121581, -0.00109695, -0.000977846, -0.000858524,
  -0.000739013, -0.00061934, -0.00049953, -0.000379611, -0.000259609,
  -0.00013955, -1.94606e-05, 0.000100633, 0.000220705, 0.000340728,
  0.000460678, 0.000580529, 0.000700254, 0.000819828, 0.000939226,
  0.00105842, 0.00117739, 0.00129611, 0.00141455, 0.00153269,
  0.0016505, 0.00176797, 0.00188506, 0.00200175, 0.00211801,
  0.00223383, 0.00234918, 0.00246404, 0.00257838, 0.00269218,
  0.00280541, 0.00291806, 0.00303011, 0.00314152, 0.00325228,
  0.00336237, 0.00347176, 0.00358043, 0.00368837, 0.00379554,
  0.00390194, 0.00400753, 0.00411231, 0.00421624, 0.00431931,
  0.00442151, 0.0045228, 0.00462317, 0.00472261, 0.00482109,
  0.00491859, 0.0050151, 0.00511061, 0.00520508, 0.00529851,
  0.00539087, 0.00548216, 0.00557235, 0.00566143, 0.00574938,
  0.00583619, 0.00592184, 0.00600631, 0.00608959, 0.00617168,
  0.00625254, 0.00633217, 0.00641056, 0.00648769, 0.00656354,
  0.00663811, 0.00671138, 0.00678334, 0.00685398, 0.00692329,
  0.00699125, 0.00705786, 0.0071231, 0.00718696, 0.00724943,
  0.00731051, 0.00737018, 0.00742843, 0.00748525, 0.00754065,
  0.0075946, 0.0076471, 0.00769814, 0.00774771, 0.00779581,
  0.00784243, 0.00788756, 0.0079312, 0.00797334, 0.00801398,
  0.0080531, 0.00809071, 0.0081268, 0.00816136, 0.00819439,
  0.00822589, 0.00825586, 0.00828428, 0.00831116, 0.00833649,
  0.00836028, 0.00838251, 0.0084032, 0.00842232, 0.0084399,
  0.00845591, 0.00847037, 0.00848327, 0.00849461, 0.0085044,
  0.00851262, 0.00851929, 0.00852441, 0.00852797, 0.00852998,
  0.00853043, 0.00852934, 0.0085267, 0.00852252, 0.0085168,
  0.00850953, 0.00850074, 0.00849041, 0.00847856, 0.00846518,
  0.00845028, 0.00843388, 0.00841596, 0.00839654, 0.00837562,
  0.00835321, 0.00832932, 0.00830394, 0.00827709, 0.00824878,
  0.008219, 0.00818778, 0.0081551, 0.008121, 0.00808546, 0.0080485,
  0.00801013, 0.00797035, 0.00792918, 0.00788662, 0.00784269,
  0.00779739, 0.00775073, 0.00770272, 0.00765338, 0.0076027,
  0.00755071, 0.00749742, 0.00744283, 0.00738695, 0.0073298,
  0.00727139, 0.00721173, 0.00715083, 0.0070887, 0.00702537,
  0.00696082, 0.00689509, 0.00682819, 0.00676012, 0.0066909,
  0.00662054, 0.00654906, 0.00647647, 0.00640278, 0.00632801,
  0.00625217, 0.00617528, 0.00609735, 0.00601839, 0.00593841,
  0.00585744, 0.00577549, 0.00569258, 0.00560871, 0.0055239,
  0.00543817, 0.00535154, 0.00526401, 0.00517561, 0.00508635,
  0.00499625, 0.00490532, 0.00481358, 0.00472104, 0.00462773,
  0.00453365, 0.00443882, 0.00434327, 0.004247, 0.00415004,
  0.00405239, 0.00395408, 0.00385513, 0.00375554, 0.00365535,
  0.00355455, 0.00345318, 0.00335125, 0.00324878, 0.00314577,
  0.00304226, 0.00293826, 0.00283378, 0.00272884, 0.00262347,
  0.00251767, 0.00241147, 0.00230488, 0.00219791, 0.0020906,
  0.00198295, 0.00187499, 0.00176673, 0.00165818, 0.00154937,
  0.00144031, 0.00133103, 0.00122153, 0.00111184, 0.00100197,
  0.000891942, 0.000781775, 0.000671484, 0.000561087, 0.000450602,
  0.000340046, 0.000229436, 0.00011879, 8.12575e-06, -0.00010254,
  -0.00021319, -0.000323806, -0.000434372, -0.00054487, -0.000655283,
  -0.000765594, -0.000875787, -0.000985843, -0.00109575, -0.00120548,
  -0.00131503, -0.00142437, -0.00153349, -0.00164238, -0.00175101,
  -0.00185937, -0.00196745, -0.00207523, -0.00218268, -0.0022898,
  -0.00239657, -0.00250298, -0.002609, -0.00271462, -0.00281983,
  -0.00292461, -0.00302894, -0.00313281, -0.00323621, -0.00333911,
  -0.00344151, -0.00354339, -0.00364473, -0.00374552, -0.00384574,
  -0.00394538, -0.00404443, -0.00414287, -0.00424069, -0.00433787,
  -0.0044344, -0.00453026, -0.00462545, -0.00471994, -0.00481373,
  -0.0049068, -0.00499913, -0.00509073, -0.00518156, -0.00527162,
  -0.0053609, -0.00544938, -0.00553706, -0.00562391, -0.00570993,
  -0.00579511, -0.00587943, -0.00596289, -0.00604546, -0.00612715,
  -0.00620793, -0.0062878, -0.00636674, -0.00644476, -0.00652182,
  -0.00659794, -0.00667308, -0.00674726, -0.00682044, -0.00689263,
  -0.00696382, -0.00703399, -0.00710314, -0.00717126, -0.00723834,
  -0.00730437, -0.00736934, -0.00743324, -0.00749606, -0.00755781,
  -0.00761846, -0.00767801, -0.00773646, -0.00779379, -0.00785001,
  -0.00790509, -0.00795904, -0.00801185, -0.00806351, -0.00811402,
  -0.00816336, -0.00821154, -0.00825855, -0.00830438, -0.00834902,
  -0.00839248, -0.00843474, -0.00847581, -0.00851567, -0.00855432,
  -0.00859176, -0.00862799, -0.00866299, -0.00869677, -0.00872932,
  -0.00876064, -0.00879073, -0.00881958, -0.00884718, -0.00887355,
  -0.00889866, -0.00892253, -0.00894515, -0.00896651, -0.00898662,
  -0.00900547, -0.00902307, -0.0090394, -0.00905447, -0.00906829,
  -0.00908084, -0.00909212, -0.00910215, -0.00911091, -0.0091184,
  -0.00912463, -0.0091296, -0.0091333, -0.00913575, -0.00913693,
  -0.00913684, -0.0091355, -0.0091329, -0.00912905, -0.00912393,
  -0.00911757, -0.00910995, -0.00910108, -0.00909096, -0.0090796,
  -0.009067, -0.00905315, -0.00903807, -0.00902176, -0.00900422,
  -0.00898544, -0.00896545, -0.00894423, -0.0089218, -0.00889816,
  -0.00887331, -0.00884726, -0.00882001, -0.00879156, -0.00876193,
  -0.00873111, -0.00869911, -0.00866594, -0.0086316, -0.0085961,
  -0.00855944, -0.00852162, -0.00848267, -0.00844257, -0.00840135,
  -0.00835899, -0.00831552, -0.00827093, -0.00822524, -0.00817845,
  -0.00813056, -0.0080816, -0.00803155, -0.00798043, -0.00792826,
  -0.00787502, -0.00782075, -0.00776543, -0.00770908, -0.00765171,
  -0.00759333, -0.00753394, -0.00747356, -0.00741219, -0.00734984,
  -0.00728652, -0.00722224, -0.00715701, -0.00709083, -0.00702372,
  -0.00695569, -0.00688675, -0.0068169, -0.00674616, -0.00667454,
  -0.00660204, -0.00652867, -0.00645446, -0.0063794, -0.0063035,
  -0.00622679, -0.00614926, -0.00607094, -0.00599182, -0.00591192,
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  -0.00560895, -0.00569282, -0.00577574, -0.00585769, -0.00593866,
  -0.00601863, -0.00609759, -0.00617553, -0.00625242, -0.00632826,
  -0.00640303, -0.00647672, -0.00654931, -0.00662079, -0.00669115,
  -0.00676037, -0.00682844, -0.00689534, -0.00696107, -0.00702561,
  -0.00708895, -0.00715108, -0.00721198, -0.00727164, -0.00733005,
  -0.0073872, -0.00744307, -0.00749766, -0.00755096, -0.00760295,
  -0.00765362, -0.00770297, -0.00775098, -0.00779764, -0.00784294,
  -0.00788687, -0.00792943, -0.0079706, -0.00801037, -0.00804875,
  -0.0080857, -0.00812124, -0.00815535, -0.00818802, -0.00821925,
  -0.00824902, -0.00827734, -0.00830419, -0.00832956, -0.00835346,
  -0.00837587, -0.00839678, -0.00841621, -0.00843412, -0.00845053,
  -0.00846543, -0.0084788, -0.00849066, -0.00850098, -0.00850978,
  -0.00851704, -0.00852277, -0.00852695, -0.00852959, -0.00853068,
  -0.00853022, -0.00852822, -0.00852466, -0.00851954, -0.00851287,
  -0.00850464, -0.00849486, -0.00848352, -0.00847062, -0.00845616,
  -0.00844014, -0.00842257, -0.00840344, -0.00838276, -0.00836053,
  -0.00833674, -0.00831141, -0.00828453, -0.0082561, -0.00822614,
  -0.00819464, -0.00816161, -0.00812704, -0.00809096, -0.00805335,
  -0.00801422, -0.00797359, -0.00793145, -0.00788781, -0.00784268,
  -0.00779606, -0.00774796, -0.00769838, -0.00764734, -0.00759484,
  -0.00754089, -0.0074855, -0.00742868, -0.00737042, -0.00731075,
  -0.00724968, -0.0071872, -0.00712334, -0.00705811, -0.0069915,
  -0.00692354, -0.00685423, -0.00678359, -0.00671163, -0.00663836,
  -0.00656379, -0.00648793, -0.0064108, -0.00633242, -0.00625279,
  -0.00617192, -0.00608984, -0.00600656, -0.00592208, -0.00583643,
  -0.00574963, -0.00566168, -0.0055726, -0.00548241, -0.00539112,
  -0.00529875, -0.00520533, -0.00511085, -0.00501535, -0.00491884,
  -0.00482133, -0.00472285, -0.00462342, -0.00452304, -0.00442175,
  -0.00431956, -0.00421649, -0.00411256, -0.00400778, -0.00390219,
  -0.00379579, -0.00368861, -0.00358068, -0.00347201, -0.00336261,
  -0.00325253, -0.00314177, -0.00303035, -0.00291831, -0.00280566,
  -0.00269242, -0.00257862, -0.00246429, -0.00234943, -0.00223408,
  -0.00211826, -0.00200199, -0.0018853, -0.00176821, -0.00165075,
  -0.00153294, -0.0014148, -0.00129636, -0.00117764, -0.00105867,
  -0.000939473, -0.000820075, -0.0007005, -0.000580775, -0.000460925,
  -0.000340975, -0.000220951, -0.00010088, 1.92139e-05, 0.000139303,
  0.000259362, 0.000379364, 0.000499284, 0.000619093, 0.000738767,
  0.000858277, 0.000977599, 0.0010967, 0.00121557, 0.00133416,
  0.00145246, 0.00157043, 0.00168805, 0.0018053, 0.00192214,
  0.00203855, 0.0021545, 0.00226997, 0.00238493, 0.00249934,
  0.00261319, 0.00272645, 0.00283909, 0.00295108, 0.0030624,
  0.00317302, 0.00328291, 0.00339204, 0.0035004, 0.00360795,
  0.00371467, 0.00382053, 0.0039255, 0.00402956, 0.00413268,
  0.00423484, 0.00433601, 0.00443617, 0.00453528, 0.00463333,
  0.00473029, 0.00482613, 0.00492083, 0.00501436, 0.0051067,
  0.00519783, 0.00528772, 0.00537634, 0.00546368, 0.0055497,
  0.0056344, 0.00571773, 0.00579969, 0.00588024, 0.00595936,
  0.00603704, 0.00611325, 0.00618797, 0.00626117, 0.00633284,
  0.00640295, 0.00647149, 0.00653844, 0.00660377, 0.00666746,
  0.0067295, 0.00678986, 0.00684853, 0.00690549, 0.00696072,
  0.00701421, 0.00706593, 0.00711587, 0.00716401, 0.00721034,
  0.00725484, 0.00729749, 0.00733829, 0.00737721, 0.00741424,
  0.00744937, 0.00748259, 0.00751387, 0.00754322, 0.00757061,
  0.00759604, 0.00761949, 0.00764095, 0.00766042, 0.00767788,
  0.00769332, 0.00770675, 0.00771813, 0.00772748, 0.00773478,
  0.00774002, 0.00774321, 0.00774432, 0.00774337, 0.00774034,
  0.00773523, 0.00772803, 0.00771874, 0.00770737, 0.0076939,
  0.00767834, 0.00766069, 0.00764094, 0.00761909, 0.00759515,
  0.00756912, 0.007541, 0.00751079, 0.0074785, 0.00744413, 0.00740768,
  0.00736916, 0.00732857, 0.00728592, 0.00724122, 0.00719447,
  0.00714569, 0.00709488, 0.00704204, 0.0069872, 0.00693036,
  0.00687153, 0.00681072, 0.00674795, 0.00668323, 0.00661657,
  0.00654798, 0.00647749, 0.0064051, 0.00633084, 0.00625472,
  0.00617675, 0.00609696, 0.00601536, 0.00593198, 0.00584683,
  0.00575993, 0.00567131, 0.00558098, 0.00548898, 0.00539531,
  0.00530002, 0.00520311, 0.00510462, 0.00500457, 0.00490299,
  0.0047999, 0.00469533, 0.00458932, 0.00448188, 0.00437305,
  0.00426285, 0.00415133, 0.0040385, 0.00392441, 0.00380908,
  0.00369254, 0.00357484, 0.00345599, 0.00333605, 0.00321503,
  0.00309299, 0.00296995, 0.00284595, 0.00272103, 0.00259523,
  0.00246858, 0.00234113, 0.00221291, 0.00208396, 0.00195432,
  0.00182404, 0.00169315, 0.0015617, 0.00142973, 0.00129728,
  0.00116439, 0.00103111, 0.000897478, 0.000763545, 0.000629352,
  0.000494944, 0.000360367, 0.000225665, 9.08864e-05, -4.39242e-05,
  -0.00017872, -0.000313453, -0.000448076, -0.000582543, -0.000716805,
  -0.000850814, -0.000984522, -0.00111788, -0.00125084, -0.00138335,
  -0.00151537, -0.00164684, -0.00177771, -0.00190795, -0.00203748,
  -0.00216628, -0.00229428, -0.00242143, -0.00254769, -0.00267301,
  -0.00279734, -0.00292062, -0.00304281, -0.00316386, -0.00328372,
  -0.00340233, -0.00351965, -0.00363563, -0.00375022, -0.00386337,
  -0.00397503, -0.00408515, -0.00419369, -0.00430059, -0.00440581,
  -0.0045093, -0.00461102, -0.0047109, -0.00480892, -0.00490502,
  -0.00499916, -0.00509129, -0.00518136, -0.00526934, -0.00535517,
  -0.00543882, -0.00552024, -0.00559939, -0.00567622, -0.0057507,
  -0.00582278, -0.00589243, -0.00595961, -0.00602427, -0.00608638,
  -0.00614591, -0.00620281, -0.00625705, -0.00630859, -0.00635741,
  -0.00640347, -0.00644674, -0.00648718, -0.00652477, -0.00655948,
  -0.00659127, -0.00662013, -0.00664603, -0.00666894, -0.00668883,
  -0.0067057, -0.0067195, -0.00673023, -0.00673787, -0.0067424,
  -0.00674379, -0.00674204, -0.00673714, -0.00672906, -0.0067178,
  -0.00670336, -0.00668571, -0.00666486, -0.00664079, -0.00661352,
  -0.00658302, -0.0065493, -0.00651237, -0.00647223, -0.00642887,
  -0.00638231, -0.00633255, -0.0062796, -0.00622347, -0.00616417,
  -0.00610173, -0.00603615, -0.00596744, -0.00589564, -0.00582077,
  -0.00574283, -0.00566187, -0.0055779, -0.00549096, -0.00540108,
  -0.00530828, -0.00521261, -0.00511409, -0.00501277, -0.00490869,
  -0.00480189, -0.00469242, -0.00458031, -0.00446563, -0.00434841,
  -0.00422871, -0.00410659, -0.00398209, -0.00385529, -0.00372624,
  -0.003595, -0.00346163, -0.00332621, -0.0031888, -0.00304947,
  -0.0029083, -0.00276536, -0.00262072, -0.00247446, -0.00232667,
  -0.00217742, -0.00202681, -0.00187491, -0.00172182, -0.00156763,
  -0.00141243, -0.00125631, -0.00109936, -0.000941696, -0.000783405,
  -0.000624592, -0.000465359, -0.000305811, -0.000146055, 1.38007e-05,
  0.000173647, 0.000333372, 0.000492863, 0.000652006, 0.000810684,
  0.000968781, 0.00112618, 0.00128276, 0.00143839, 0.00159297,
  0.00174636, 0.00189843, 0.00204908, 0.00219816, 0.00234555,
  0.00249112, 0.00263475, 0.00277631, 0.00291566, 0.00305268,
  0.00318723, 0.00331919, 0.00344843, 0.00357481, 0.0036982,
  0.00381848, 0.00393551, 0.00404917, 0.00415932, 0.00426584,
  0.0043686, 0.00446747, 0.00456233, 0.00465305, 0.00473952,
  0.0048216, 0.00489918, 0.00497215, 0.00504038, 0.00510376,
  0.00516218, 0.00521554, 0.00526372, 0.00530662, 0.00534415,
  0.00537621, 0.00540269, 0.00542353, 0.00543861, 0.00544788,
  0.00545125, 0.00544864, 0.00543999, 0.00542525, 0.00540434,
  0.00537722, 0.00534385, 0.00530418, 0.00525819, 0.00520584,
  0.00514712, 0.00508201, 0.00501052, 0.00493264, 0.00484839,
  0.0047578, 0.00466088, 0.00455768, 0.00444825, 0.00433265,
  0.00421095, 0.00408322, 0.00394956, 0.00381008, 0.00366488,
  0.0035141, 0.00335787, 0.00319635, 0.00302971, 0.00285813,
  0.00268181, 0.00250095, 0.00231579, 0.00212656, 0.00193353,
  0.00173698, 0.00153719, 0.00133449, 0.0011292, 0.000921677,
  0.000712289, 0.000501428, 0.000289507, 7.69605e-05, -0.000135755,
  -0.000348161, -0.000559753, -0.000770004, -0.000978362, -0.00118425,
  -0.00138706, -0.00158616, -0.0017809, -0.00197059, -0.00215451,
  -0.0023319, -0.00250201, -0.00266401, -0.00281706, -0.0029603,
  -0.0030928, -0.00321363, -0.0033218, -0.00341631, -0.00349609,
  -0.00356005, -0.00360706, -0.00363595, -0.0036455, -0.00363445,
  -0.00360151, -0.00354533, -0.00346451, -0.00335763, -0.0032232,
  -0.00305967, -0.00286548, -0.00263898, -0.00237848, -0.00208225,
  -0.00174849, -0.00137535, -0.000960915, -0.000503223, -2.4671e-07};
  const G4double G4ParticleHPFastLegendre::l19[4001] = {-1, -0.907221,
  -0.818793, -0.734581, -0.654452, -0.578277, -0.505931, -0.437291,
  -0.372236, -0.310648, -0.252415, -0.197422, -0.145562, -0.0967284,
  -0.0508163, -0.00772479, 0.0326452, 0.07039, 0.105604, 0.138378,
  0.168803, 0.196965, 0.22295, 0.246839, 0.268715, 0.288655, 0.306735,
  0.323032, 0.337616, 0.350559, 0.361929, 0.371793, 0.380217,
  0.387263, 0.392993, 0.397467, 0.400743, 0.402878, 0.403926,
  0.403941, 0.402974, 0.401076, 0.398296, 0.394681, 0.390276,
  0.385127, 0.379277, 0.372766, 0.365637, 0.357929, 0.349678,
  0.340923, 0.331698, 0.322039, 0.311978, 0.301548, 0.290779,
  0.279703, 0.268348, 0.256742, 0.244912, 0.232884, 0.220683,
  0.208334, 0.195859, 0.183281, 0.170622, 0.157902, 0.145142, 0.13236,
  0.119574, 0.106802, 0.0940615, 0.0813678, 0.0687364, 0.0561821,
  0.0437188, 0.0313599, 0.0191182, 0.00700568, -0.00496608,
  -0.0167862, -0.0284443, -0.0399306, -0.0512359, -0.0623514,
  -0.073269, -0.0839809, -0.0944799, -0.104759, -0.114813, -0.124634,
  -0.134218, -0.14356, -0.152655, -0.161499, -0.170088, -0.178419,
  -0.186488, -0.194293, -0.201832, -0.209101, -0.2161, -0.222827,
  -0.229281, -0.23546, -0.241365, -0.246995, -0.252349, -0.257429,
  -0.262233, -0.266764, -0.271021, -0.275006, -0.278721, -0.282165,
  -0.285342, -0.288252, -0.290899, -0.293283, -0.295408, -0.297276,
  -0.298889, -0.30025, -0.301362, -0.302229, -0.302852, -0.303236,
  -0.303383, -0.303298, -0.302983, -0.302443, -0.301681, -0.3007,
  -0.299505, -0.298101, -0.296489, -0.294676, -0.292664, -0.290458,
  -0.288063, -0.285483, -0.282721, -0.279782, -0.276671, -0.273392,
  -0.26995, -0.266348, -0.262592, -0.258686, -0.254634, -0.250441,
  -0.246111, -0.241649, -0.23706, -0.232347, -0.227516, -0.222571,
  -0.217516, -0.212356, -0.207095, -0.201738, -0.196289, -0.190753,
  -0.185133, -0.179435, -0.173662, -0.167819, -0.16191, -0.155939,
  -0.149911, -0.143829, -0.137698, -0.131522, -0.125304, -0.119049,
  -0.11276, -0.106442, -0.100099, -0.0937333, -0.0873497, -0.0809516,
  -0.0745427, -0.0681267, -0.0617069, -0.055287, -0.0488703,
  -0.0424602, -0.0360601, -0.0296731, -0.0233026, -0.0169517,
  -0.0106234, -0.00432088, 0.00195298, 0.00819522, 0.014403,
  0.0205735, 0.0267039, 0.0327916, 0.038834, 0.0448284, 0.0507724,
  0.0566635, 0.0624994, 0.0682777, 0.073996, 0.0796523, 0.0852444,
  0.0907701, 0.0962275, 0.101615, 0.106929, 0.11217, 0.117335,
  0.122422, 0.12743, 0.132357, 0.137201, 0.141962, 0.146637, 0.151225,
  0.155725, 0.160136, 0.164456, 0.168684, 0.172819, 0.17686, 0.180806,
  0.184657, 0.18841, 0.192066, 0.195623, 0.199081, 0.202439, 0.205696,
  0.208853, 0.211908, 0.21486, 0.21771, 0.220457, 0.223101, 0.225641,
  0.228077, 0.230409, 0.232636, 0.23476, 0.236779, 0.238693, 0.240503,
  0.242208, 0.243809, 0.245306, 0.246699, 0.247988, 0.249173,
  0.250256, 0.251235, 0.252111, 0.252886, 0.253558, 0.254129, 0.2546,
  0.25497, 0.255241, 0.255412, 0.255485, 0.25546, 0.255338, 0.255119,
  0.254805, 0.254396, 0.253893, 0.253296, 0.252608, 0.251827,
  0.250956, 0.249995, 0.248946, 0.247809, 0.246585, 0.245275, 0.24388,
  0.242402, 0.240841, 0.239199, 0.237476, 0.235674, 0.233794,
  0.231837, 0.229804, 0.227696, 0.225516, 0.223263, 0.220939,
  0.218545, 0.216083, 0.213554, 0.210959, 0.208299, 0.205577,
  0.202792, 0.199947, 0.197042, 0.194079, 0.19106, 0.187986, 0.184857,
  0.181677, 0.178445, 0.175163, 0.171832, 0.168455, 0.165032,
  0.161565, 0.158055, 0.154503, 0.150912, 0.147281, 0.143613, 0.13991,
  0.136172, 0.1324, 0.128597, 0.124764, 0.120901, 0.117011, 0.113095,
  0.109154, 0.10519, 0.101203, 0.0971958, 0.0931691, 0.0891244,
  0.085063, 0.0809863, 0.0768956, 0.0727922, 0.0686775, 0.0645528,
  0.0604194, 0.0562785, 0.0521316, 0.0479798, 0.0438244, 0.0396667,
  0.035508, 0.0313496, 0.0271925, 0.0230381, 0.0188877, 0.0147423,
  0.0106032, 0.00647157, 0.0023486, -0.00176456, -0.00586675,
  -0.00995684, -0.0140337, -0.0180962, -0.0221433, -0.0261739,
  -0.0301868, -0.0341811, -0.0381557, -0.0421095, -0.0460415,
  -0.0499508, -0.0538362, -0.0576969, -0.0615319, -0.0653402,
  -0.0691208, -0.072873, -0.0765956, -0.0802879, -0.083949, -0.087578,
  -0.091174, -0.0947362, -0.0982638, -0.101756, -0.105212, -0.108631,
  -0.112012, -0.115355, -0.118659, -0.121923, -0.125146, -0.128327,
  -0.131467, -0.134564, -0.137618, -0.140629, -0.143594, -0.146515,
  -0.14939, -0.152218, -0.155, -0.157735, -0.160422, -0.163061,
  -0.165651, -0.168192, -0.170683, -0.173124, -0.175515, -0.177855,
  -0.180143, -0.18238, -0.184565, -0.186698, -0.188778, -0.190805,
  -0.192779, -0.194699, -0.196566, -0.198378, -0.200136, -0.20184,
  -0.20349, -0.205084, -0.206623, -0.208108, -0.209536, -0.21091,
  -0.212228, -0.21349, -0.214697, -0.215848, -0.216943, -0.217982,
  -0.218965, -0.219892, -0.220764, -0.221579, -0.222338, -0.223042,
  -0.22369, -0.224282, -0.224819, -0.2253, -0.225725, -0.226096,
  -0.226411, -0.226671, -0.226876, -0.227026, -0.227122, -0.227163,
  -0.22715, -0.227083, -0.226963, -0.226789, -0.226562, -0.226282,
  -0.225949, -0.225563, -0.225126, -0.224636, -0.224096, -0.223503,
  -0.22286, -0.222167, -0.221423, -0.220629, -0.219786, -0.218894,
  -0.217953, -0.216964, -0.215927, -0.214842, -0.213711, -0.212532,
  -0.211308, -0.210037, -0.208722, -0.207361, -0.205956, -0.204508,
  -0.203015, -0.20148, -0.199903, -0.198283, -0.196622, -0.19492,
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  -0.0358516, -0.0337924, -0.0317281, -0.0296587, -0.0275846,
  -0.0255059, -0.023423, -0.0213361, -0.0192453, -0.017151,
  -0.0150535, -0.0129528, -0.0108494, -0.00874345, -0.00663519,
  -0.00452489, -0.00241279, -0.000299153, 0.00181577, 0.00393174,
  0.00604848, 0.00816575, 0.0102833, 0.0124008, 0.0145182, 0.016635,
  0.018751, 0.0208661, 0.0229799, 0.0250921, 0.0272026, 0.029311,
  0.0314171, 0.0335207, 0.0356214, 0.0377191, 0.0398134, 0.0419041,
  0.043991, 0.0460738, 0.0481521, 0.0502259, 0.0522947, 0.0543584,
  0.0564166, 0.0584692, 0.0605159, 0.0625563, 0.0645904, 0.0666177,
  0.068638, 0.0706512, 0.0726568, 0.0746547, 0.0766446, 0.0786263,
  0.0805995, 0.0825639, 0.0845193, 0.0864655, 0.0884021, 0.090329,
  0.0922459, 0.0941525, 0.0960485, 0.0979338, 0.0998081, 0.101671,
  0.103523, 0.105362, 0.10719, 0.109006, 0.110809, 0.112599, 0.114377,
  0.116141, 0.117891, 0.119628, 0.121352, 0.123061, 0.124755,
  0.126435, 0.1281, 0.129751, 0.131385, 0.133005, 0.134608, 0.136196,
  0.137767, 0.139322, 0.140861, 0.142382, 0.143887, 0.145374,
  0.146843, 0.148295, 0.14973, 0.151146, 0.152543, 0.153922, 0.155283,
  0.156625, 0.157947, 0.15925, 0.160534, 0.161798, 0.163042, 0.164266,
  0.16547, 0.166653, 0.167816, 0.168958, 0.170079, 0.171179, 0.172258,
  0.173315, 0.17435, 0.175364, 0.176356, 0.177326, 0.178273, 0.179198,
  0.1801, 0.18098, 0.181837, 0.182671, 0.183481, 0.184269, 0.185033,
  0.185773, 0.18649, 0.187183, 0.187852, 0.188497, 0.189117, 0.189714,
  0.190286, 0.190833, 0.191356, 0.191854, 0.192328, 0.192776,
  0.193199, 0.193598, 0.193971, 0.194318, 0.194641, 0.194938,
  0.195209, 0.195455, 0.195675, 0.19587, 0.196038, 0.196181, 0.196298,
  0.196389, 0.196454, 0.196493, 0.196505, 0.196492, 0.196452,
  0.196386, 0.196294, 0.196176, 0.196031, 0.19586, 0.195663, 0.195439,
  0.195189, 0.194912, 0.194609, 0.19428, 0.193925, 0.193543, 0.193134,
  0.192699, 0.192238, 0.191751, 0.191238, 0.190698, 0.190132,
  0.189539, 0.188921, 0.188276, 0.187606, 0.186909, 0.186187,
  0.185438, 0.184664, 0.183864, 0.183038, 0.182187, 0.18131, 0.180407,
  0.17948, 0.178526, 0.177548, 0.176545, 0.175516, 0.174463, 0.173384,
  0.172281, 0.171154, 0.170002, 0.168825, 0.167625, 0.1664, 0.165151,
  0.163878, 0.162582, 0.161262, 0.159918, 0.158552, 0.157162,
  0.155749, 0.154313, 0.152855, 0.151374, 0.14987, 0.148345, 0.146798,
  0.145228, 0.143637, 0.142025, 0.140391, 0.138737, 0.137061,
  0.135365, 0.133648, 0.131911, 0.130154, 0.128378, 0.126581,
  0.124765, 0.12293, 0.121076, 0.119203, 0.117312, 0.115403, 0.113475,
  0.11153, 0.109567, 0.107587, 0.10559, 0.103576, 0.101545, 0.0994982,
  0.0974354, 0.0953568, 0.0932628, 0.0911536, 0.0890294, 0.0868906,
  0.0847375, 0.0825702, 0.0803891, 0.0781945, 0.0759867, 0.073766,
  0.0715326, 0.0692869, 0.0670292, 0.0647597, 0.0624788, 0.0601868,
  0.057884, 0.0555707, 0.0532472, 0.0509139, 0.048571, 0.0462189,
  0.0438579, 0.0414884, 0.0391106, 0.036725, 0.0343318, 0.0319313,
  0.0295239, 0.02711, 0.0246899, 0.0222639, 0.0198324, 0.0173957,
  0.0149542, 0.0125082, 0.010058, 0.00760413, 0.0051468, 0.0026864,
  0.000223301, -0.00224215, -0.00470958, -0.00717864, -0.00964897,
  -0.0121202, -0.0145919, -0.0170639, -0.0195356, -0.0220067,
  -0.0244769, -0.0269458, -0.029413, -0.0318782, -0.0343409,
  -0.0368009, -0.0392576, -0.0417108, -0.0441601, -0.0466051,
  -0.0490454, -0.0514807, -0.0539105, -0.0563345, -0.0587523,
  -0.0611635, -0.0635678, -0.0659648, -0.0683541, -0.0707353,
  -0.0731081, -0.075472, -0.0778267, -0.0801718, -0.082507,
  -0.0848318, -0.0871459, -0.0894488, -0.0917404, -0.09402,
  -0.0962875, -0.0985424, -0.100784, -0.103013, -0.105228, -0.107428,
  -0.109615, -0.111786, -0.113943, -0.116083, -0.118208, -0.120317,
  -0.122409, -0.124484, -0.126541, -0.128581, -0.130603, -0.132607,
  -0.134591, -0.136557, -0.138503, -0.140429, -0.142335, -0.144221,
  -0.146086, -0.147929, -0.149751, -0.151552, -0.15333, -0.155085,
  -0.156818, -0.158528, -0.160214, -0.161876, -0.163514, -0.165128,
  -0.166717, -0.168281, -0.16982, -0.171333, -0.17282, -0.174281,
  -0.175715, -0.177122, -0.178503, -0.179856, -0.181181, -0.182478,
  -0.183748, -0.184988, -0.1862, -0.187383, -0.188537, -0.189661,
  -0.190756, -0.19182, -0.192854, -0.193858, -0.194831, -0.195773,
  -0.196684, -0.197564, -0.198412, -0.199228, -0.200012, -0.200764,
  -0.201483, -0.20217, -0.202824, -0.203446, -0.204033, -0.204588,
  -0.205109, -0.205597, -0.20605, -0.20647, -0.206856, -0.207207,
  -0.207524, -0.207806, -0.208054, -0.208267, -0.208445, -0.208588,
  -0.208695, -0.208768, -0.208805, -0.208807, -0.208774, -0.208704,
  -0.2086, -0.208459, -0.208283, -0.20807, -0.207822, -0.207538,
  -0.207218, -0.206862, -0.20647, -0.206042, -0.205578, -0.205078,
  -0.204542, -0.20397, -0.203361, -0.202717, -0.202036, -0.20132,
  -0.200568, -0.199779, -0.198955, -0.198095, -0.1972, -0.196268,
  -0.195301, -0.194299, -0.193261, -0.192188, -0.191079, -0.189935,
  -0.188757, -0.187543, -0.186295, -0.185012, -0.183694, -0.182342,
  -0.180956, -0.179536, -0.178081, -0.176594, -0.175072, -0.173517,
  -0.171929, -0.170308, -0.168655, -0.166968, -0.16525, -0.163499,
  -0.161717, -0.159902, -0.158057, -0.15618, -0.154272, -0.152334,
  -0.150365, -0.148366, -0.146338, -0.14428, -0.142192, -0.140076,
  -0.137931, -0.135758, -0.133557, -0.131328, -0.129072, -0.126789,
  -0.124479, -0.122144, -0.119782, -0.117394, -0.114982, -0.112545,
  -0.110083, -0.107597, -0.105088, -0.102556, -0.1, -0.0974227,
  -0.0948231, -0.092202, -0.0895597, -0.0868968, -0.0842136,
  -0.0815107, -0.0787885, -0.0760474, -0.0732879, -0.0705105,
  -0.0677157, -0.0649039, -0.0620756, -0.0592314, -0.0563716,
  -0.0534969, -0.0506078, -0.0477046, -0.0447881, -0.0418586,
  -0.0389167, -0.035963, -0.0329979, -0.0300221, -0.0270361,
  -0.0240403, -0.0210355, -0.0180221, -0.0150006, -0.0119717,
  -0.008936, -0.00589397, -0.00284622, 0.000206663, 0.00326409,
  0.00632548, 0.00939023, 0.0124577, 0.0155274, 0.0185987, 0.0216709,
  0.0247435, 0.0278158, 0.0308872, 0.0339571, 0.037025, 0.0400901,
  0.0431518, 0.0462096, 0.0492627, 0.0523106, 0.0553527, 0.0583882,
  0.0614166, 0.0644372, 0.0674493, 0.0704524, 0.0734459, 0.0764289,
  0.079401, 0.0823614, 0.0853096, 0.0882448, 0.0911665, 0.094074,
  0.0969666, 0.0998436, 0.102705, 0.105549, 0.108375, 0.111184,
  0.113974, 0.116744, 0.119495, 0.122224, 0.124933, 0.127619,
  0.130283, 0.132924, 0.135541, 0.138133, 0.1407, 0.143241, 0.145756,
  0.148244, 0.150705, 0.153137, 0.15554, 0.157914, 0.160257, 0.16257,
  0.164852, 0.167102, 0.169319, 0.171503, 0.173653, 0.17577, 0.177851,
  0.179897, 0.181906, 0.18388, 0.185816, 0.187714, 0.189574, 0.191396,
  0.193178, 0.19492, 0.196622, 0.198283, 0.199903, 0.20148, 0.203015,
  0.204508, 0.205956, 0.207361, 0.208722, 0.210037, 0.211308,
  0.212532, 0.213711, 0.214842, 0.215927, 0.216964, 0.217953,
  0.218894, 0.219786, 0.220629, 0.221423, 0.222167, 0.22286, 0.223503,
  0.224096, 0.224636, 0.225126, 0.225563, 0.225949, 0.226282,
  0.226562, 0.226789, 0.226963, 0.227083, 0.22715, 0.227163, 0.227122,
  0.227026, 0.226876, 0.226671, 0.226411, 0.226096, 0.225725, 0.2253,
  0.224819, 0.224282, 0.22369, 0.223042, 0.222338, 0.221579, 0.220764,
  0.219892, 0.218965, 0.217982, 0.216943, 0.215848, 0.214697, 0.21349,
  0.212228, 0.21091, 0.209536, 0.208108, 0.206623, 0.205084, 0.20349,
  0.20184, 0.200136, 0.198378, 0.196566, 0.194699, 0.192779, 0.190805,
  0.188778, 0.186698, 0.184565, 0.18238, 0.180143, 0.177855, 0.175515,
  0.173124, 0.170683, 0.168192, 0.165651, 0.163061, 0.160422,
  0.157735, 0.155, 0.152218, 0.14939, 0.146515, 0.143594, 0.140629,
  0.137618, 0.134564, 0.131467, 0.128327, 0.125146, 0.121923,
  0.118659, 0.115355, 0.112012, 0.108631, 0.105212, 0.101756,
  0.0982638, 0.0947362, 0.091174, 0.087578, 0.083949, 0.0802879,
  0.0765956, 0.072873, 0.0691208, 0.0653402, 0.0615319, 0.0576969,
  0.0538362, 0.0499508, 0.0460415, 0.0421095, 0.0381557, 0.0341811,
  0.0301868, 0.0261739, 0.0221433, 0.0180962, 0.0140337, 0.00995684,
  0.00586675, 0.00176456, -0.0023486, -0.00647157, -0.0106032,
  -0.0147423, -0.0188877, -0.0230381, -0.0271925, -0.0313496,
  -0.035508, -0.0396667, -0.0438244, -0.0479798, -0.0521316,
  -0.0562785, -0.0604194, -0.0645528, -0.0686775, -0.0727922,
  -0.0768956, -0.0809863, -0.085063, -0.0891244, -0.0931691,
  -0.0971958, -0.101203, -0.10519, -0.109154, -0.113095, -0.117011,
  -0.120901, -0.124764, -0.128597, -0.1324, -0.136172, -0.13991,
  -0.143613, -0.147281, -0.150912, -0.154503, -0.158055, -0.161565,
  -0.165032, -0.168455, -0.171832, -0.175163, -0.178445, -0.181677,
  -0.184857, -0.187986, -0.19106, -0.194079, -0.197042, -0.199947,
  -0.202792, -0.205577, -0.208299, -0.210959, -0.213554, -0.216083,
  -0.218545, -0.220939, -0.223263, -0.225516, -0.227696, -0.229804,
  -0.231837, -0.233794, -0.235674, -0.237476, -0.239199, -0.240841,
  -0.242402, -0.24388, -0.245275, -0.246585, -0.247809, -0.248946,
  -0.249995, -0.250956, -0.251827, -0.252608, -0.253296, -0.253893,
  -0.254396, -0.254805, -0.255119, -0.255338, -0.25546, -0.255485,
  -0.255412, -0.255241, -0.25497, -0.2546, -0.254129, -0.253558,
  -0.252886, -0.252111, -0.251235, -0.250256, -0.249173, -0.247988,
  -0.246699, -0.245306, -0.243809, -0.242208, -0.240503, -0.238693,
  -0.236779, -0.23476, -0.232636, -0.230409, -0.228077, -0.225641,
  -0.223101, -0.220457, -0.21771, -0.21486, -0.211908, -0.208853,
  -0.205696, -0.202439, -0.199081, -0.195623, -0.192066, -0.18841,
  -0.184657, -0.180806, -0.17686, -0.172819, -0.168684, -0.164456,
  -0.160136, -0.155725, -0.151225, -0.146637, -0.141962, -0.137201,
  -0.132357, -0.12743, -0.122422, -0.117335, -0.11217, -0.106929,
  -0.101615, -0.0962275, -0.0907701, -0.0852444, -0.0796523,
  -0.073996, -0.0682777, -0.0624994, -0.0566635, -0.0507724,
  -0.0448284, -0.038834, -0.0327916, -0.0267039, -0.0205735,
  -0.014403, -0.00819522, -0.00195298, 0.00432088, 0.0106234,
  0.0169517, 0.0233026, 0.0296731, 0.0360601, 0.0424602, 0.0488703,
  0.055287, 0.0617069, 0.0681267, 0.0745427, 0.0809516, 0.0873497,
  0.0937333, 0.100099, 0.106442, 0.11276, 0.119049, 0.125304,
  0.131522, 0.137698, 0.143829, 0.149911, 0.155939, 0.16191, 0.167819,
  0.173662, 0.179435, 0.185133, 0.190753, 0.196289, 0.201738,
  0.207095, 0.212356, 0.217516, 0.222571, 0.227516, 0.232347, 0.23706,
  0.241649, 0.246111, 0.250441, 0.254634, 0.258686, 0.262592,
  0.266348, 0.26995, 0.273392, 0.276671, 0.279782, 0.282721, 0.285483,
  0.288063, 0.290458, 0.292664, 0.294676, 0.296489, 0.298101,
  0.299505, 0.3007, 0.301681, 0.302443, 0.302983, 0.303298, 0.303383,
  0.303236, 0.302852, 0.302229, 0.301362, 0.30025, 0.298889, 0.297276,
  0.295408, 0.293283, 0.290899, 0.288252, 0.285342, 0.282165,
  0.278721, 0.275006, 0.271021, 0.266764, 0.262233, 0.257429,
  0.252349, 0.246995, 0.241365, 0.23546, 0.229281, 0.222827, 0.2161,
  0.209101, 0.201832, 0.194293, 0.186488, 0.178419, 0.170088,
  0.161499, 0.152655, 0.14356, 0.134218, 0.124634, 0.114813, 0.104759,
  0.0944799, 0.0839809, 0.073269, 0.0623514, 0.0512359, 0.0399306,
  0.0284443, 0.0167862, 0.00496608, -0.00700568, -0.0191182,
  -0.0313599, -0.0437188, -0.0561821, -0.0687364, -0.0813678,
  -0.0940615, -0.106802, -0.119574, -0.13236, -0.145142, -0.157902,
  -0.170622, -0.183281, -0.195859, -0.208334, -0.220683, -0.232884,
  -0.244912, -0.256742, -0.268348, -0.279703, -0.290779, -0.301548,
  -0.311978, -0.322039, -0.331698, -0.340923, -0.349678, -0.357929,
  -0.365637, -0.372766, -0.379277, -0.385127, -0.390276, -0.394681,
  -0.398296, -0.401076, -0.402974, -0.403941, -0.403926, -0.402878,
  -0.400743, -0.397467, -0.392993, -0.387263, -0.380217, -0.371793,
  -0.361929, -0.350559, -0.337616, -0.323032, -0.306735, -0.288655,
  -0.268715, -0.246839, -0.22295, -0.196965, -0.168803, -0.138378,
  -0.105604, -0.07039, -0.0326452, 0.00772479, 0.0508163, 0.0967284,
  0.145562, 0.197422, 0.252415, 0.310648, 0.372236, 0.437291,
  0.505931, 0.578277, 0.654452, 0.734581, 0.818793, 0.907221, 1};
  const G4double G4ParticleHPFastLegendre::i19[4001] = {0, -0.000476615,
  -0.000907935, -0.0012961, -0.00164319, -0.0019512, -0.00222209,
  -0.00245774, -0.00265997, -0.00283054, -0.00297117, -0.00308349,
  -0.0031691, -0.00322955, -0.00326631, -0.00328083, -0.00327448,
  -0.00324861, -0.00320451, -0.00314341, -0.00306652, -0.00297498,
  -0.00286991, -0.00275237, -0.0026234, -0.00248397, -0.00233505,
  -0.00217753, -0.0020123, -0.00184019, -0.001662, -0.0014785,
  -0.00129044, -0.00109851, -0.000903394, -0.000705726, -0.000506124,
  -0.00030517, -0.000103424, 9.85859e-05, 0.000300356, 0.000501407,
  0.000701287, 0.000899566, 0.00109584, 0.00128972, 0.00148085,
  0.00166889, 0.00185352, 0.00203443, 0.00221135, 0.00238403,
  0.0025522, 0.00271565, 0.00287417, 0.00302757, 0.00317567,
  0.0033183, 0.00345532, 0.00358661, 0.00371203, 0.00383149,
  0.00394488, 0.00405214, 0.0041532, 0.00424799, 0.00433646,
  0.0044186, 0.00449436, 0.00456374, 0.00462672, 0.00468331,
  0.00473353, 0.00477738, 0.00481491, 0.00484613, 0.0048711,
  0.00488987, 0.00490248, 0.00490901, 0.00490951, 0.00490407,
  0.00489275, 0.00487565, 0.00485285, 0.00482444, 0.00479053,
  0.00475121, 0.00470658, 0.00465677, 0.00460186, 0.00454199,
  0.00447727, 0.00440781, 0.00433375, 0.0042552, 0.00417229,
  0.00408515, 0.00399391, 0.00389871, 0.00379966, 0.00369692,
  0.00359061, 0.00348086, 0.00336783, 0.00325163, 0.00313241,
  0.00301031, 0.00288546, 0.002758, 0.00262808, 0.00249582,
  0.00236136, 0.00222484, 0.0020864, 0.00194616, 0.00180427,
  0.00166086, 0.00151607, 0.00137001, 0.00122282, 0.00107464,
  0.000925591, 0.000775795, 0.000625381, 0.000474473, 0.000323193,
  0.000171661, 1.99958e-05, -0.000131684, -0.000283264, -0.00043463,
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  -0.00747074, -0.0074423, -0.00741235, -0.00738088, -0.00734791,
  -0.00731344, -0.00727746, -0.00723999, -0.00720103, -0.00716059,
  -0.00711868, -0.00707529, -0.00703043, -0.00698412, -0.00693636,
  -0.00688716, -0.00683652, -0.00678446, -0.00673097, -0.00667608,
  -0.00661979, -0.00656211, -0.00650305, -0.00644262, -0.00638083,
  -0.00631769, -0.00625322, -0.00618741, -0.0061203, -0.00605188,
  -0.00598217, -0.00591118, -0.00583893, -0.00576543, -0.00569069,
  -0.00561473, -0.00553756, -0.00545919, -0.00537965, -0.00529894,
  -0.00521708, -0.00513409, -0.00504999, -0.00496478, -0.00487849,
  -0.00479113, -0.00470273, -0.00461329, -0.00452284, -0.00443139,
  -0.00433896, -0.00424558, -0.00415125, -0.00405601, -0.00395986,
  -0.00386284, -0.00376495, -0.00366622, -0.00356668, -0.00346633,
  -0.0033652, -0.00326332, -0.0031607, -0.00305737, -0.00295335,
  -0.00284866, -0.00274332, -0.00263736, -0.00253079, -0.00242365,
  -0.00231596, -0.00220773, -0.002099, -0.00198979, -0.00188012,
  -0.00177001, -0.0016595, -0.0015486, -0.00143734, -0.00132574,
  -0.00121384, -0.00110166, -0.000989213, -0.000876539, -0.000763659,
  -0.000650599, -0.000537386, -0.000424045, -0.000310605,
  -0.000197091, -8.35305e-05, 3.00501e-05, 0.000143624, 0.000257163,
  0.000370641, 0.000484029, 0.000597302, 0.000710431, 0.000823389,
  0.000936147, 0.00104868, 0.00116096, 0.00127295, 0.00138464,
  0.00149599, 0.00160697, 0.00171756, 0.00182772, 0.00193744,
  0.00204668, 0.00215541, 0.00226361, 0.00237125, 0.0024783,
  0.00258473, 0.00269052, 0.00279563, 0.00290004, 0.00300373,
  0.00310666, 0.0032088, 0.00331014, 0.00341064, 0.00351027,
  0.00360901, 0.00370682, 0.0038037, 0.00389959, 0.00399449,
  0.00408836, 0.00418118, 0.00427292, 0.00436355, 0.00445305,
  0.0045414, 0.00462856, 0.00471451, 0.00479924, 0.0048827,
  0.00496488, 0.00504575, 0.00512529, 0.00520348, 0.00528028,
  0.00535569, 0.00542967, 0.0055022, 0.00557325, 0.00564282,
  0.00571086, 0.00577737, 0.00584233, 0.0059057, 0.00596746,
  0.00602761, 0.00608612, 0.00614296, 0.00619812, 0.00625159,
  0.00630333, 0.00635334, 0.00640159, 0.00644807, 0.00649276,
  0.00653564, 0.0065767, 0.00661592, 0.00665329, 0.00668879,
  0.00672241, 0.00675412, 0.00678393, 0.00681182, 0.00683777,
  0.00686176, 0.0068838, 0.00690387, 0.00692196, 0.00693805,
  0.00695214, 0.00696422, 0.00697428, 0.00698231, 0.00698831,
  0.00699227, 0.00699418, 0.00699403, 0.00699183, 0.00698756,
  0.00698122, 0.00697281, 0.00696233, 0.00694978, 0.00693514,
  0.00691843, 0.00689963, 0.00687876, 0.00685581, 0.00683078,
  0.00680368, 0.0067745, 0.00674326, 0.00670995, 0.00667458,
  0.00663716, 0.00659769, 0.00655618, 0.00651263, 0.00646705,
  0.00641946, 0.00636986, 0.00631826, 0.00626468, 0.00620911,
  0.00615158, 0.00609211, 0.00603069, 0.00596735, 0.0059021,
  0.00583495, 0.00576593, 0.00569505, 0.00562232, 0.00554777,
  0.00547142, 0.00539328, 0.00531337, 0.00523172, 0.00514834,
  0.00506327, 0.00497652, 0.00488811, 0.00479808, 0.00470645,
  0.00461323, 0.00451847, 0.00442218, 0.0043244, 0.00422515,
  0.00412446, 0.00402237, 0.0039189, 0.00381408, 0.00370795,
  0.00360054, 0.00349188, 0.003382, 0.00327095, 0.00315875,
  0.00304544, 0.00293107, 0.00281565, 0.00269924, 0.00258187,
  0.00246358, 0.00234441, 0.0022244, 0.00210358, 0.00198201,
  0.00185971, 0.00173675, 0.00161314, 0.00148895, 0.00136421,
  0.00123897, 0.00111327, 0.000987158, 0.000860678, 0.000733877,
  0.000606801, 0.000479496, 0.000352011, 0.000224393, 9.66891e-05,
  -3.10513e-05, -0.00015878, -0.000286447, -0.000414004, -0.000541401,
  -0.000668588, -0.000795514, -0.000922129, -0.00104838, -0.00117422,
  -0.0012996, -0.00142446, -0.00154876, -0.00167243, -0.00179544,
  -0.00191772, -0.00203923, -0.00215991, -0.00227972, -0.00239859,
  -0.00251648, -0.00263333, -0.0027491, -0.00286372, -0.00297716,
  -0.00308935, -0.00320024, -0.00330979, -0.00341793, -0.00352463,
  -0.00362982, -0.00373347, -0.0038355, -0.00393589, -0.00403457,
  -0.0041315, -0.00422662, -0.00431989, -0.00441126, -0.00450068,
  -0.0045881, -0.00467348, -0.00475677, -0.00483792, -0.00491689,
  -0.00499364, -0.0050681, -0.00514026, -0.00521005, -0.00527745,
  -0.0053424, -0.00540486, -0.0054648, -0.00552218, -0.00557696,
  -0.0056291, -0.00567857, -0.00572532, -0.00576932, -0.00581055,
  -0.00584897, -0.00588454, -0.00591723, -0.00594703, -0.00597389,
  -0.00599779, -0.00601871, -0.00603662, -0.00605149, -0.00606331,
  -0.00607206, -0.00607771, -0.00608025, -0.00607966, -0.00607592,
  -0.00606903, -0.00605897, -0.00604572, -0.00602929, -0.00600966,
  -0.00598683, -0.00596079, -0.00593154, -0.00589908, -0.00586342,
  -0.00582454, -0.00578247, -0.0057372, -0.00568874, -0.0056371,
  -0.0055823, -0.00552434, -0.00546325, -0.00539905, -0.00533174,
  -0.00526136, -0.00518792, -0.00511145, -0.00503199, -0.00494955,
  -0.00486418, -0.0047759, -0.00468476, -0.00459078, -0.00449402,
  -0.00439451, -0.0042923, -0.00418743, -0.00407996, -0.00396993,
  -0.0038574, -0.00374243, -0.00362508, -0.00350539, -0.00338345,
  -0.0032593, -0.00313303, -0.00300469, -0.00287437, -0.00274213,
  -0.00260805, -0.0024722, -0.00233468, -0.00219556, -0.00205493,
  -0.00191287, -0.00176947, -0.00162483, -0.00147905, -0.0013322,
  -0.0011844, -0.00103575, -0.000886336, -0.000736275, -0.000585671,
  -0.00043463, -0.000283264, -0.000131684, 1.99958e-05, 0.000171661,
  0.000323193, 0.000474473, 0.000625381, 0.000775795, 0.000925591,
  0.00107464, 0.00122282, 0.00137001, 0.00151607, 0.00166086,
  0.00180427, 0.00194616, 0.0020864, 0.00222484, 0.00236136,
  0.00249582, 0.00262808, 0.002758, 0.00288546, 0.00301031,
  0.00313241, 0.00325163, 0.00336783, 0.00348086, 0.00359061,
  0.00369692, 0.00379966, 0.00389871, 0.00399391, 0.00408515,
  0.00417229, 0.0042552, 0.00433375, 0.00440781, 0.00447727,
  0.00454199, 0.00460186, 0.00465677, 0.00470658, 0.00475121,
  0.00479053, 0.00482444, 0.00485285, 0.00487565, 0.00489275,
  0.00490407, 0.00490951, 0.00490901, 0.00490248, 0.00488987,
  0.0048711, 0.00484613, 0.00481491, 0.00477738, 0.00473353,
  0.00468331, 0.00462672, 0.00456374, 0.00449436, 0.0044186,
  0.00433646, 0.00424799, 0.0041532, 0.00405214, 0.00394488,
  0.00383149, 0.00371203, 0.00358661, 0.00345532, 0.0033183,
  0.00317567, 0.00302757, 0.00287417, 0.00271565, 0.0025522,
  0.00238403, 0.00221135, 0.00203443, 0.00185352, 0.00166889,
  0.00148085, 0.00128972, 0.00109584, 0.000899566, 0.000701287,
  0.000501407, 0.000300356, 9.85859e-05, -0.000103424, -0.00030517,
  -0.000506124, -0.000705726, -0.000903394, -0.00109851, -0.00129044,
  -0.0014785, -0.001662, -0.00184019, -0.0020123, -0.00217753,
  -0.00233505, -0.00248397, -0.0026234, -0.00275237, -0.00286991,
  -0.00297498, -0.00306652, -0.00314341, -0.00320451, -0.00324861,
  -0.00327448, -0.00328083, -0.00326631, -0.00322955, -0.0031691,
  -0.00308349, -0.00297117, -0.00283054, -0.00265997, -0.00245774,
  -0.00222209, -0.0019512, -0.00164319, -0.0012961, -0.000907935,
  -0.000476615, 8.29415e-17}; const G4double
  G4ParticleHPFastLegendre::l20[4201] = {1, 0.902461, 0.809737,
  0.72167, 0.638107, 0.558898, 0.483895, 0.412957, 0.345943, 0.282719,
  0.223152, 0.167113, 0.114475, 0.0651177, 0.01892, -0.0242339,
  -0.0644574, -0.101861, -0.136552, -0.168634, -0.198211, -0.225381,
  -0.250239, -0.272882, -0.293398, -0.311878, -0.328407, -0.343069,
  -0.355946, -0.367117, -0.376659, -0.384646, -0.391152, -0.396246,
  -0.399997, -0.402472, -0.403734, -0.403846, -0.402869, -0.40086,
  -0.397878, -0.393977, -0.38921, -0.383629, -0.377284, -0.370224,
  -0.362494, -0.35414, -0.345206, -0.335735, -0.325766, -0.315339,
  -0.304492, -0.293262, -0.281684, -0.269792, -0.257619, -0.245196,
  -0.232554, -0.219722, -0.206728, -0.193599, -0.180361, -0.167039,
  -0.153656, -0.140235, -0.126799, -0.113367, -0.099961, -0.0865988,
  -0.073299, -0.0600789, -0.046955, -0.0339431, -0.021058,
  -0.00831404, 0.00427544, 0.0166977, 0.0289407, 0.0409932, 0.0528444,
  0.0644844, 0.0759037, 0.0870934, 0.0980455, 0.108752, 0.119206,
  0.129402, 0.139332, 0.148991, 0.158375, 0.167479, 0.176298,
  0.184829, 0.193069, 0.201015, 0.208664, 0.216014, 0.223064,
  0.229812, 0.236257, 0.242399, 0.248238, 0.253772, 0.259003,
  0.263931, 0.268557, 0.272882, 0.276907, 0.280634, 0.284065,
  0.287202, 0.290047, 0.292602, 0.29487, 0.296855, 0.298558, 0.299984,
  0.301135, 0.302016, 0.302629, 0.302978, 0.303068, 0.302903,
  0.302486, 0.301822, 0.300915, 0.29977, 0.298391, 0.296783, 0.294951,
  0.292899, 0.290632, 0.288155, 0.285473, 0.282591, 0.279515,
  0.276248, 0.272797, 0.269166, 0.265361, 0.261386, 0.257247, 0.25295,
  0.248499, 0.2439, 0.239157, 0.234277, 0.229263, 0.224123, 0.21886,
  0.213479, 0.207987, 0.202388, 0.196687, 0.19089, 0.185001, 0.179025,
  0.172968, 0.166834, 0.160628, 0.154355, 0.148021, 0.141629,
  0.135184, 0.128691, 0.122155, 0.115581, 0.108972, 0.102333,
  0.0956688, 0.0889837, 0.0822817, 0.0755673, 0.0688444, 0.0621173,
  0.0553898, 0.0486661, 0.0419499, 0.0352452, 0.0285557, 0.021885,
  0.0152368, 0.00861467, 0.00202207, -0.00453757, -0.0110609,
  -0.0175447, -0.0239857, -0.0303809, -0.036727, -0.0430213,
  -0.0492607, -0.0554424, -0.0615637, -0.0676219, -0.0736143,
  -0.0795384, -0.0853917, -0.0911718, -0.0968764, -0.102503, -0.10805,
  -0.113515, -0.118896, -0.12419, -0.129397, -0.134514, -0.139539,
  -0.144471, -0.149308, -0.154049, -0.158692, -0.163235, -0.167678,
  -0.172018, -0.176256, -0.180389, -0.184417, -0.188338, -0.192152,
  -0.195858, -0.199454, -0.202941, -0.206317, -0.209581, -0.212734,
  -0.215774, -0.218702, -0.221516, -0.224217, -0.226803, -0.229275,
  -0.231633, -0.233877, -0.236006, -0.23802, -0.239919, -0.241704,
  -0.243374, -0.244931, -0.246373, -0.247701, -0.248915, -0.250017,
  -0.251005, -0.251882, -0.252646, -0.253299, -0.253841, -0.254273,
  -0.254596, -0.254809, -0.254914, -0.254912, -0.254804, -0.254589,
  -0.25427, -0.253847, -0.25332, -0.252692, -0.251962, -0.251132,
  -0.250203, -0.249176, -0.248052, -0.246832, -0.245518, -0.24411,
  -0.24261, -0.241019, -0.239338, -0.237569, -0.235713, -0.23377,
  -0.231744, -0.229634, -0.227442, -0.22517, -0.222818, -0.220389,
  -0.217884, -0.215305, -0.212652, -0.209927, -0.207132, -0.204269,
  -0.201338, -0.198341, -0.19528, -0.192157, -0.188972, -0.185728,
  -0.182426, -0.179067, -0.175654, -0.172187, -0.168669, -0.1651,
  -0.161483, -0.157819, -0.15411, -0.150357, -0.146562, -0.142727,
  -0.138852, -0.134941, -0.130993, -0.127012, -0.122997, -0.118952,
  -0.114878, -0.110776, -0.106647, -0.102494, -0.0983176, -0.0941199,
  -0.0899021, -0.0856659, -0.0814128, -0.0771444, -0.0728621,
  -0.0685675, -0.0642621, -0.0599474, -0.0556248, -0.0512959,
  -0.0469621, -0.0426248, -0.0382856, -0.0339458, -0.0296069,
  -0.0252702, -0.0209372, -0.0166093, -0.0122878, -0.00797403,
  -0.00366943, 0.0006247, 0.00490706, 0.00917633, 0.0134312,
  0.0176705, 0.0218929, 0.0260971, 0.030282, 0.0344463, 0.0385888,
  0.0427083, 0.0468038, 0.0508739, 0.0549177, 0.058934, 0.0629217,
  0.0668796, 0.0708069, 0.0747024, 0.078565, 0.0823938, 0.0861878,
  0.0899461, 0.0936676, 0.0973514, 0.100997, 0.104602, 0.108168,
  0.111692, 0.115174, 0.118613, 0.122008, 0.125359, 0.128665,
  0.131924, 0.135137, 0.138302, 0.141419, 0.144488, 0.147507,
  0.150475, 0.153393, 0.15626, 0.159074, 0.161836, 0.164545, 0.167201,
  0.169802, 0.172349, 0.174841, 0.177277, 0.179658, 0.181982,
  0.184249, 0.186459, 0.188612, 0.190707, 0.192744, 0.194722,
  0.196642, 0.198503, 0.200305, 0.202047, 0.203729, 0.205352,
  0.206915, 0.208417, 0.209859, 0.211241, 0.212562, 0.213822,
  0.215022, 0.216161, 0.217239, 0.218256, 0.219212, 0.220108,
  0.220942, 0.221716, 0.222429, 0.223082, 0.223673, 0.224205,
  0.224676, 0.225086, 0.225437, 0.225727, 0.225958, 0.22613, 0.226242,
  0.226294, 0.226288, 0.226224, 0.2261, 0.225919, 0.22568, 0.225383,
  0.225029, 0.224618, 0.224151, 0.223627, 0.223047, 0.222412,
  0.221722, 0.220977, 0.220177, 0.219324, 0.218417, 0.217457,
  0.216445, 0.21538, 0.214264, 0.213096, 0.211878, 0.21061, 0.209292,
  0.207925, 0.206509, 0.205045, 0.203533, 0.201975, 0.20037, 0.198719,
  0.197022, 0.195281, 0.193496, 0.191667, 0.189796, 0.187882,
  0.185926, 0.183929, 0.181892, 0.179815, 0.177698, 0.175544,
  0.173351, 0.171121, 0.168855, 0.166552, 0.164215, 0.161843,
  0.159437, 0.156998, 0.154526, 0.152023, 0.149488, 0.146923,
  0.144329, 0.141706, 0.139054, 0.136375, 0.133669, 0.130936,
  0.128179, 0.125397, 0.12259, 0.119761, 0.116909, 0.114035, 0.111141,
  0.108226, 0.105291, 0.102338, 0.0993663, 0.0963774, 0.0933719,
  0.0903505, 0.0873139, 0.0842628, 0.081198, 0.0781202, 0.0750302,
  0.0719286, 0.0688163, 0.0656938, 0.062562, 0.0594216, 0.0562733,
  0.0531177, 0.0499557, 0.046788, 0.0436152, 0.0404381, 0.0372573,
  0.0340736, 0.0308878, 0.0277003, 0.0245121, 0.0213237, 0.0181359,
  0.0149494, 0.0117647, 0.00858269, 0.00540394, 0.00222915,
  -0.000941033, -0.00410593, -0.00726489, -0.0104173, -0.0135624,
  -0.0166996, -0.0198283, -0.0229479, -0.0260576, -0.029157,
  -0.0322452, -0.0353219, -0.0383863, -0.0414378, -0.0444758,
  -0.0474998, -0.0505091, -0.0535033, -0.0564816, -0.0594435,
  -0.0623885, -0.065316, -0.0682254, -0.0711163, -0.073988, -0.07684,
  -0.0796719, -0.082483, -0.085273, -0.0880411, -0.0907871,
  -0.0935103, -0.0962103, -0.0988867, -0.101539, -0.104166, -0.106769,
  -0.109346, -0.111897, -0.114421, -0.116919, -0.119389, -0.121832,
  -0.124246, -0.126632, -0.128989, -0.131317, -0.133615, -0.135884,
  -0.138121, -0.140328, -0.142504, -0.144649, -0.146762, -0.148842,
  -0.15089, -0.152906, -0.154888, -0.156837, -0.158753, -0.160634,
  -0.162482, -0.164295, -0.166073, -0.167816, -0.169524, -0.171197,
  -0.172834, -0.174435, -0.176001, -0.17753, -0.179022, -0.180478,
  -0.181897, -0.183279, -0.184624, -0.185931, -0.187201, -0.188434,
  -0.189628, -0.190785, -0.191904, -0.192985, -0.194027, -0.195032,
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  -0.184149, -0.183842, -0.183513, -0.183162, -0.182788, -0.182393,
  -0.181975, -0.181535, -0.181074, -0.18059, -0.180084, -0.179557,
  -0.179007, -0.178436, -0.177843, -0.177228, -0.176592, -0.175933,
  -0.175254, -0.174552, -0.17383, -0.173086, -0.17232, -0.171533,
  -0.170725, -0.169896, -0.169046, -0.168175, -0.167283, -0.16637,
  -0.165437, -0.164483, -0.163508, -0.162513, -0.161497, -0.160462,
  -0.159406, -0.15833, -0.157234, -0.156118, -0.154983, -0.153828,
  -0.152654, -0.15146, -0.150247, -0.149015, -0.147764, -0.146494,
  -0.145205, -0.143898, -0.142572, -0.141228, -0.139866, -0.138486,
  -0.137088, -0.135672, -0.134239, -0.132789, -0.131321, -0.129836,
  -0.128334, -0.126815, -0.12528, -0.123728, -0.12216, -0.120576,
  -0.118977, -0.117361, -0.11573, -0.114083, -0.112422, -0.110745,
  -0.109054, -0.107348, -0.105627, -0.103893, -0.102144, -0.100381,
  -0.0986053, -0.0968158, -0.0950131, -0.0931974, -0.091369,
  -0.0895279, -0.0876745, -0.085809, -0.0839315, -0.0820424,
  -0.0801417, -0.0782299, -0.0763069, -0.0743732, -0.0724289,
  -0.0704743, -0.0685096, -0.0665349, -0.0645507, -0.062557,
  -0.0605542, -0.0585424, -0.056522, -0.0544931, -0.0524561,
  -0.0504111, -0.0483584, -0.0462982, -0.0442309, -0.0421566,
  -0.0400756, -0.0379882, -0.0358947, -0.0337952, -0.03169,
  -0.0295794, -0.0274637, -0.0253432, -0.023218, -0.0210884,
  -0.0189548, -0.0168174, -0.0146764, -0.0125322, -0.0103849,
  -0.00823488, -0.00608241, -0.00392775, -0.00177116, 0.000387071,
  0.00254667, 0.00470737, 0.00686889, 0.00903096, 0.0111933,
  0.0133556, 0.0155176, 0.0176791, 0.0198397, 0.0219992, 0.0241572,
  0.0263136, 0.028468, 0.0306202, 0.0327698, 0.0349166, 0.0370603,
  0.0392006, 0.0413373, 0.04347, 0.0455985, 0.0477224, 0.0498416,
  0.0519557, 0.0540644, 0.0561675, 0.0582647, 0.0603556, 0.0624401,
  0.0645178, 0.0665884, 0.0686518, 0.0707074, 0.0727552, 0.0747949,
  0.076826, 0.0788485, 0.0808619, 0.0828661, 0.0848606, 0.0868454,
  0.08882, 0.0907842, 0.0927377, 0.0946804, 0.0966118, 0.0985317,
  0.10044, 0.102336, 0.10422, 0.106091, 0.10795, 0.109795, 0.111627,
  0.113445, 0.11525, 0.11704, 0.118816, 0.120577, 0.122324, 0.124055,
  0.125771, 0.127471, 0.129155, 0.130823, 0.132474, 0.134109,
  0.135727, 0.137328, 0.138912, 0.140477, 0.142025, 0.143555,
  0.145066, 0.146559, 0.148033, 0.149488, 0.150924, 0.15234, 0.153737,
  0.155114, 0.15647, 0.157806, 0.159122, 0.160417, 0.161691, 0.162943,
  0.164174, 0.165384, 0.166572, 0.167738, 0.168882, 0.170003,
  0.171102, 0.172178, 0.173231, 0.174261, 0.175268, 0.176251,
  0.177211, 0.178146, 0.179058, 0.179946, 0.180809, 0.181648,
  0.182463, 0.183253, 0.184017, 0.184757, 0.185472, 0.186161,
  0.186825, 0.187463, 0.188075, 0.188662, 0.189222, 0.189757,
  0.190265, 0.190747, 0.191203, 0.191632, 0.192034, 0.19241, 0.192759,
  0.193081, 0.193376, 0.193644, 0.193884, 0.194098, 0.194284,
  0.194442, 0.194574, 0.194677, 0.194753, 0.194802, 0.194822,
  0.194815, 0.194781, 0.194718, 0.194627, 0.194509, 0.194363,
  0.194188, 0.193986, 0.193756, 0.193498, 0.193211, 0.192897,
  0.192555, 0.192184, 0.191786, 0.191359, 0.190905, 0.190422,
  0.189912, 0.189374, 0.188808, 0.188214, 0.187592, 0.186942,
  0.186265, 0.18556, 0.184827, 0.184067, 0.183279, 0.182464, 0.181621,
  0.180751, 0.179854, 0.17893, 0.177978, 0.177, 0.175995, 0.174963,
  0.173905, 0.17282, 0.171708, 0.17057, 0.169406, 0.168216, 0.167,
  0.165759, 0.164491, 0.163198, 0.16188, 0.160536, 0.159168, 0.157774,
  0.156356, 0.154913, 0.153445, 0.151954, 0.150438, 0.148898,
  0.147335, 0.145748, 0.144138, 0.142505, 0.140849, 0.13917, 0.137469,
  0.135745, 0.134, 0.132232, 0.130443, 0.128633, 0.126801, 0.124948,
  0.123075, 0.121181, 0.119267, 0.117334, 0.11538, 0.113407, 0.111415,
  0.109404, 0.107375, 0.105327, 0.103261, 0.101177, 0.0990762,
  0.0969578, 0.0948225, 0.0926705, 0.0905023, 0.088318, 0.086118,
  0.0839025, 0.081672, 0.0794268, 0.077167, 0.0748931, 0.0726054,
  0.0703042, 0.0679898, 0.0656626, 0.0633229, 0.0609711, 0.0586074,
  0.0562323, 0.0538461, 0.051449, 0.0490416, 0.0466241, 0.0441969,
  0.0417604, 0.0393149, 0.0368607, 0.0343984, 0.0319281, 0.0294503,
  0.0269655, 0.0244738, 0.0219758, 0.0194718, 0.0169622, 0.0144474,
  0.0119277, 0.00940363, 0.00687548, 0.00434367, 0.00180859,
  -0.000729345, -0.00326975, -0.00581223, -0.00835637, -0.0109018,
  -0.013448, -0.0159947, -0.0185415, -0.0210879, -0.0236335,
  -0.026178, -0.0287208, -0.0312616, -0.0338, -0.0363356, -0.0388679,
  -0.0413966, -0.0439211, -0.0464412, -0.0489563, -0.0514661,
  -0.0539701, -0.056468, -0.0589592, -0.0614434, -0.0639202,
  -0.0663891, -0.0688497, -0.0713017, -0.0737444, -0.0761777,
  -0.078601, -0.0810138, -0.0834159, -0.0858068, -0.088186,
  -0.0905531, -0.0929077, -0.0952495, -0.0975779, -0.0998926,
  -0.102193, -0.104479, -0.10675, -0.109006, -0.111246, -0.113469,
  -0.115676, -0.117866, -0.120039, -0.122194, -0.12433, -0.126448,
  -0.128547, -0.130626, -0.132686, -0.134725, -0.136744, -0.138742,
  -0.140718, -0.142673, -0.144606, -0.146516, -0.148403, -0.150267,
  -0.152107, -0.153923, -0.155715, -0.157482, -0.159224, -0.16094,
  -0.162631, -0.164296, -0.165934, -0.167545, -0.169129, -0.170685,
  -0.172214, -0.173714, -0.175186, -0.176629, -0.178043, -0.179427,
  -0.180782, -0.182106, -0.1834, -0.184664, -0.185896, -0.187097,
  -0.188267, -0.189405, -0.19051, -0.191583, -0.192624, -0.193631,
  -0.194606, -0.195547, -0.196454, -0.197327, -0.198166, -0.198971,
  -0.199741, -0.200477, -0.201177, -0.201842, -0.202471, -0.203065,
  -0.203623, -0.204145, -0.20463, -0.205079, -0.205492, -0.205868,
  -0.206206, -0.206508, -0.206773, -0.207, -0.207189, -0.207341,
  -0.207456, -0.207532, -0.20757, -0.207571, -0.207533, -0.207457,
  -0.207342, -0.207189, -0.206997, -0.206767, -0.206499, -0.206191,
  -0.205845, -0.20546, -0.205036, -0.204574, -0.204073, -0.203532,
  -0.202953, -0.202336, -0.201679, -0.200983, -0.200249, -0.199476,
  -0.198664, -0.197814, -0.196925, -0.195998, -0.195032, -0.194027,
  -0.192985, -0.191904, -0.190785, -0.189628, -0.188434, -0.187201,
  -0.185931, -0.184624, -0.183279, -0.181897, -0.180478, -0.179022,
  -0.17753, -0.176001, -0.174435, -0.172834, -0.171197, -0.169524,
  -0.167816, -0.166073, -0.164295, -0.162482, -0.160634, -0.158753,
  -0.156837, -0.154888, -0.152906, -0.15089, -0.148842, -0.146762,
  -0.144649, -0.142504, -0.140328, -0.138121, -0.135884, -0.133615,
  -0.131317, -0.128989, -0.126632, -0.124246, -0.121832, -0.119389,
  -0.116919, -0.114421, -0.111897, -0.109346, -0.106769, -0.104166,
  -0.101539, -0.0988867, -0.0962103, -0.0935103, -0.0907871,
  -0.0880411, -0.085273, -0.082483, -0.0796719, -0.07684, -0.073988,
  -0.0711163, -0.0682254, -0.065316, -0.0623885, -0.0594435,
  -0.0564816, -0.0535033, -0.0505091, -0.0474998, -0.0444758,
  -0.0414378, -0.0383863, -0.0353219, -0.0322452, -0.029157,
  -0.0260576, -0.0229479, -0.0198283, -0.0166996, -0.0135624,
  -0.0104173, -0.00726489, -0.00410593, -0.000941033, 0.00222915,
  0.00540394, 0.00858269, 0.0117647, 0.0149494, 0.0181359, 0.0213237,
  0.0245121, 0.0277003, 0.0308878, 0.0340736, 0.0372573, 0.0404381,
  0.0436152, 0.046788, 0.0499557, 0.0531177, 0.0562733, 0.0594216,
  0.062562, 0.0656938, 0.0688163, 0.0719286, 0.0750302, 0.0781202,
  0.081198, 0.0842628, 0.0873139, 0.0903505, 0.0933719, 0.0963774,
  0.0993663, 0.102338, 0.105291, 0.108226, 0.111141, 0.114035,
  0.116909, 0.119761, 0.12259, 0.125397, 0.128179, 0.130936, 0.133669,
  0.136375, 0.139054, 0.141706, 0.144329, 0.146923, 0.149488,
  0.152023, 0.154526, 0.156998, 0.159437, 0.161843, 0.164215,
  0.166552, 0.168855, 0.171121, 0.173351, 0.175544, 0.177698,
  0.179815, 0.181892, 0.183929, 0.185926, 0.187882, 0.189796,
  0.191667, 0.193496, 0.195281, 0.197022, 0.198719, 0.20037, 0.201975,
  0.203533, 0.205045, 0.206509, 0.207925, 0.209292, 0.21061, 0.211878,
  0.213096, 0.214264, 0.21538, 0.216445, 0.217457, 0.218417, 0.219324,
  0.220177, 0.220977, 0.221722, 0.222412, 0.223047, 0.223627,
  0.224151, 0.224618, 0.225029, 0.225383, 0.22568, 0.225919, 0.2261,
  0.226224, 0.226288, 0.226294, 0.226242, 0.22613, 0.225958, 0.225727,
  0.225437, 0.225086, 0.224676, 0.224205, 0.223673, 0.223082,
  0.222429, 0.221716, 0.220942, 0.220108, 0.219212, 0.218256,
  0.217239, 0.216161, 0.215022, 0.213822, 0.212562, 0.211241,
  0.209859, 0.208417, 0.206915, 0.205352, 0.203729, 0.202047,
  0.200305, 0.198503, 0.196642, 0.194722, 0.192744, 0.190707,
  0.188612, 0.186459, 0.184249, 0.181982, 0.179658, 0.177277,
  0.174841, 0.172349, 0.169802, 0.167201, 0.164545, 0.161836,
  0.159074, 0.15626, 0.153393, 0.150475, 0.147507, 0.144488, 0.141419,
  0.138302, 0.135137, 0.131924, 0.128665, 0.125359, 0.122008,
  0.118613, 0.115174, 0.111692, 0.108168, 0.104602, 0.100997,
  0.0973514, 0.0936676, 0.0899461, 0.0861878, 0.0823938, 0.078565,
  0.0747024, 0.0708069, 0.0668796, 0.0629217, 0.058934, 0.0549177,
  0.0508739, 0.0468038, 0.0427083, 0.0385888, 0.0344463, 0.030282,
  0.0260971, 0.0218929, 0.0176705, 0.0134312, 0.00917633, 0.00490706,
  0.0006247, -0.00366943, -0.00797403, -0.0122878, -0.0166093,
  -0.0209372, -0.0252702, -0.0296069, -0.0339458, -0.0382856,
  -0.0426248, -0.0469621, -0.0512959, -0.0556248, -0.0599474,
  -0.0642621, -0.0685675, -0.0728621, -0.0771444, -0.0814128,
  -0.0856659, -0.0899021, -0.0941199, -0.0983176, -0.102494,
  -0.106647, -0.110776, -0.114878, -0.118952, -0.122997, -0.127012,
  -0.130993, -0.134941, -0.138852, -0.142727, -0.146562, -0.150357,
  -0.15411, -0.157819, -0.161483, -0.1651, -0.168669, -0.172187,
  -0.175654, -0.179067, -0.182426, -0.185728, -0.188972, -0.192157,
  -0.19528, -0.198341, -0.201338, -0.204269, -0.207132, -0.209927,
  -0.212652, -0.215305, -0.217884, -0.220389, -0.222818, -0.22517,
  -0.227442, -0.229634, -0.231744, -0.23377, -0.235713, -0.237569,
  -0.239338, -0.241019, -0.24261, -0.24411, -0.245518, -0.246832,
  -0.248052, -0.249176, -0.250203, -0.251132, -0.251962, -0.252692,
  -0.25332, -0.253847, -0.25427, -0.254589, -0.254804, -0.254912,
  -0.254914, -0.254809, -0.254596, -0.254273, -0.253841, -0.253299,
  -0.252646, -0.251882, -0.251005, -0.250017, -0.248915, -0.247701,
  -0.246373, -0.244931, -0.243374, -0.241704, -0.239919, -0.23802,
  -0.236006, -0.233877, -0.231633, -0.229275, -0.226803, -0.224217,
  -0.221516, -0.218702, -0.215774, -0.212734, -0.209581, -0.206317,
  -0.202941, -0.199454, -0.195858, -0.192152, -0.188338, -0.184417,
  -0.180389, -0.176256, -0.172018, -0.167678, -0.163235, -0.158692,
  -0.154049, -0.149308, -0.144471, -0.139539, -0.134514, -0.129397,
  -0.12419, -0.118896, -0.113515, -0.10805, -0.102503, -0.0968764,
  -0.0911718, -0.0853917, -0.0795384, -0.0736143, -0.0676219,
  -0.0615637, -0.0554424, -0.0492607, -0.0430213, -0.036727,
  -0.0303809, -0.0239857, -0.0175447, -0.0110609, -0.00453757,
  0.00202207, 0.00861467, 0.0152368, 0.021885, 0.0285557, 0.0352452,
  0.0419499, 0.0486661, 0.0553898, 0.0621173, 0.0688444, 0.0755673,
  0.0822817, 0.0889837, 0.0956688, 0.102333, 0.108972, 0.115581,
  0.122155, 0.128691, 0.135184, 0.141629, 0.148021, 0.154355,
  0.160628, 0.166834, 0.172968, 0.179025, 0.185001, 0.19089, 0.196687,
  0.202388, 0.207987, 0.213479, 0.21886, 0.224123, 0.229263, 0.234277,
  0.239157, 0.2439, 0.248499, 0.25295, 0.257247, 0.261386, 0.265361,
  0.269166, 0.272797, 0.276248, 0.279515, 0.282591, 0.285473,
  0.288155, 0.290632, 0.292899, 0.294951, 0.296783, 0.298391, 0.29977,
  0.300915, 0.301822, 0.302486, 0.302903, 0.303068, 0.302978,
  0.302629, 0.302016, 0.301135, 0.299984, 0.298558, 0.296855, 0.29487,
  0.292602, 0.290047, 0.287202, 0.284065, 0.280634, 0.276907,
  0.272882, 0.268557, 0.263931, 0.259003, 0.253772, 0.248238,
  0.242399, 0.236257, 0.229812, 0.223064, 0.216014, 0.208664,
  0.201015, 0.193069, 0.184829, 0.176298, 0.167479, 0.158375,
  0.148991, 0.139332, 0.129402, 0.119206, 0.108752, 0.0980455,
  0.0870934, 0.0759037, 0.0644844, 0.0528444, 0.0409932, 0.0289407,
  0.0166977, 0.00427544, -0.00831404, -0.021058, -0.0339431,
  -0.046955, -0.0600789, -0.073299, -0.0865988, -0.099961, -0.113367,
  -0.126799, -0.140235, -0.153656, -0.167039, -0.180361, -0.193599,
  -0.206728, -0.219722, -0.232554, -0.245196, -0.257619, -0.269792,
  -0.281684, -0.293262, -0.304492, -0.315339, -0.325766, -0.335735,
  -0.345206, -0.35414, -0.362494, -0.370224, -0.377284, -0.383629,
  -0.38921, -0.393977, -0.397878, -0.40086, -0.402869, -0.403846,
  -0.403734, -0.402472, -0.399997, -0.396246, -0.391152, -0.384646,
  -0.376659, -0.367117, -0.355946, -0.343069, -0.328407, -0.311878,
  -0.293398, -0.272882, -0.250239, -0.225381, -0.198211, -0.168634,
  -0.136552, -0.101861, -0.0644574, -0.0242339, 0.01892, 0.0651177,
  0.114475, 0.167113, 0.223152, 0.282719, 0.345943, 0.412957,
  0.483895, 0.558898, 0.638107, 0.72167, 0.809737, 0.902461, 1};
  const G4double G4ParticleHPFastLegendre::i20[4201] = {0, 0.000452767,
  0.000860239, 0.00122467, 0.00154825, 0.00183307, 0.00208119,
  0.00229456, 0.00247509, 0.00262462, 0.00274492, 0.0028377,
  0.00290461, 0.00294724, 0.00296712, 0.00296573, 0.0029445,
  0.00290478, 0.00284791, 0.00277514, 0.0026877, 0.00258675,
  0.00247341, 0.00234877, 0.00221386, 0.00206966, 0.00191713,
  0.00175718, 0.00159068, 0.00141845, 0.0012413, 0.00105997,
  0.000875202, 0.00068767, 0.000498034, 0.000306919, 0.000114917,
  -7.74095e-05, -0.000269528, -0.000460933, -0.000651147,
  -0.000839721, -0.00102623, -0.00121027, -0.00139147, -0.00156948,
  -0.00174396, -0.00191461, -0.00208115, -0.0022433, -0.00240082,
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